Prove that the product of any two consecutive integers is even

Answers

Answer 1

Answer:

Credit: Luqman Khan

Explanation:

n(n+1)

n^2+n

check first case n=1

1+1=2 2(1)

it works for first case

assume true for n=k

k^2+k=2A

check n=k+1

(k+1)^2+(k+1)

k^2+2k+1+k+1

k^2+3k+2

k^2+k+2k+2

2A+2k+2

2(A+K+2)

It works for first case. If it works for n=k, then it also works for n=k+1

Then it is true for all 2 consecutive numbers, by mathematical induction


Related Questions

What would the population size of sika deer be one year after the carrying capacity increased to 70,000 as a result of deforestation? assume rmax does not change.

Answers

The population size of Sika deer one year after the carrying capacity increased to 70000 as a result of deforestation is; 63667 deer

How to Calculate Growth Rate?

We are given the following about the Sika deer population;

Initial Population in 2005 = 26000

Stabilized Population between 2012 and 2014 = 58000

r_max for population = 0.57

Now, we want to find the population size of Sika deer one year after the carrying capacity increased to 70000 as a result of deforestation

Thus;

carrying capacity; k = 70000

population size; N = 58000

max growth rate; r_max = 0.57

Formula for the growth is;

dN/dt = (r_max × N)[(K - N)/K]

Plugging in the relevant values gives;

dN/dt = 0.57 × 58000[12000/70000]

dN/dt = 5667

Thus;

Increase in population = 5667 + 58000

⇒ 63667

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Tyler ate a cheeseburger from a fast food restaurant for dinner, and he was awake all night feeling sick. now, just thinking about eating any fast food makes him feel nauseous, and he is certain that he will never want to eat it again. tyler’s aversion to fast food can best be explained by

Answers

Tyler’s aversion to fast food, who feel nauseous just thinking about eating fast food, can best be explained by stimulus generalization.

What is the meaning of the term “stimulus generalization”?

The stimulus generalization is the quality of mind to perform a task in a new condition, in such way that is learned in the similar but different situation happen in the past.

Tyler ate a cheeseburger from a fast food restaurant for dinner, and he was awake all night feeling sick.

Now, just thinking about eating any fast food makes him feel nauseous, and he is certain that he will never want to eat it again.

Let understand why he is feeling nauseous in such condition-

He ate a cheeseburger (type of fast food) in the past.This fast food make him sick.Now his behavior against eating any fast food is changed.He learned that, eating fast food can make him sick.This is a example of stimulus generalization.

Thus, the Tyler’s aversion to fast food, who feel nauseous just thinking about eating fast food can best be explained by stimulus generalization.

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Identify two things that differentiate depression from sadness. (site 1) brainly

Answers

Depression is something that is diagnosed, and more so a longer term. An emotion of sadness can be often, but is not considered a mental illness.

This hybrid uses metric formats to tell a true story.

Answers

Precision is a hybrid element that uses metric formats to tell a true story.

What is a true story?

A true story is also referred to as non-fiction and it can be defined as a literary work (story) that is written to describe and provide information to readers based on facts and reality.

This utimately implies that, a true story (non-fiction) is both informative, true and factual in nature.

In English literature, precision is a hybrid element that uses metric formats to tell a true story.

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Someone who is applying for a loan from a bank can expect the bank to:

Answers

Answer: aceitar o pedido de empréstimo

Explanation:

Which candidate will most likely get the job? samuel hayley rhonda enrique

Answers

Answer:

hayley

Explanation:

took test

Compare the perspectives of the narrator and her first employers regarding wages. what does this comparison reveal about how they view immigrant labor?

Answers

The comparison is that the narrator believes that wage is important for a job while the first employers believed that asking a question about wages was a sign of disrespect.

Who is a Narrator?

This refers to a person that tells a story or the events of action and their order of occurrence.

Hence, we can see what this reveals about how they view immigrant labor is that the narrator believes this would help her get freedom from oppression and poverty, while the first employers are of the opinion that immigrant labor is one that should be taken advantage of.

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One possible reason that the revolutionary-era poets used the

Answers

Answer:

One possible reason that the Revolutionary-era poets used the iambic meter was to imitate the classical style.

Explanation:

As the Revolutionary-era poets were inspired Classical era, they wrote using the iambic meter, which consists on two syllables where the first one was unstressed, and the one following it was stressed.

Choose all of the items that are associated with great society programs

Answers

Answer:

medicare and medicaid

Explanation:

usatestprep

Answer: Medicare, Medicaid, and Head Start

Explanation: I had this question and answered it correctly.

You created a photo album with transitions and want to send it to friends, but the file size is too large for email. how can you use one command to fix this?

Answers

A command you can use to fix this is to: use the Share feature in Backstage view to create a pdf document and then send it as an attachment.

How to reduce the size of a picture?

In a scenario where you created a photo album with transitions that you wish to send to your friends but you get an error that the file size is too large to be sent via email or other forms of internet transfer.

Thus, a command that you can use to fix this issue is to use the Share feature in Backstage view of your software application to create a pdf document and then send it to your friends as an attachment via email.

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Determine whether the statement is true or false. d dx (tan2(x)) = d dx (sec2(x))

Answers

This statement is true

A high school drama club is putting on their annual theater production

Answers

Answer:

what

Explanation:

what is the question

Consider the following reaction: no(g) + so3(g) ⇌ no2(g) + so2(g) a reaction mixture initially contains 2.0 bar no2 and 1.0 bar so2. determine the equilibrium pressure of so2 if kp for the reaction at this temperature is 0.0118.

Answers

The equilibrium pressure for the sulfur dioxide in the reaction has been 0.0843 bar.

What is equilibrium?

The equilibrium is the condition in which the partial pressure of the product and the reactant molecules is equal.

The ICE table for the partial pressure is attached.

Based on the pressure of equilibrium, the pressure constant is given as:


[tex]k_p=\rm \dfrac{[pNO]\;[pSO_2]}{[pNO][pSO_3]}\\0.0118=\dfrac{a^2}{(0.86-a)^2}\\a=0.0843[/tex]

Thus, the partial pressure of sulfur dioxide at equilibrium is 0.0843 bar.

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The negatively charged balloon is brought near the two cans. what happens?

Answers

Answer:

The negatively charged balloon (from rubbing against hair) will repel the electrons of paper/water/aluminum cans away from the spot closest to the balloon, resulting in a positive charge on the paper/water/aluminum can.

Explanation:

41 1 describe two ways how social media platforms are abused

Answers

Answer:

People can spread false information and people can upload explicit, inappropriate pictures.

Explanation:

False information - Sometimes people can abuse social media by spreading rumors about people, or causing mayhem that may not be factually correct. You should look out for this and avoid it by using credible sources and checking the website credentials.

Explicit Images and Videos - People can also abuse social media platforms by posting things that are not fit for the general environment. A good rule is make choices that build others up and support them!

Costs which are always relevant in decision making are those costs which are:

Answers

Answer:

Differential, avoidable, and opportunity

What context clue best helps readers determine the meaning of the word standard? ""numerous"" ""rigidly fixed"" ""tea-time"" ""subject""

Answers

The context clue which best helps readers to determine the meaning of the word standard is: B. "rigidly fixed"

What is a context clue?

A context clue can be defined as hints that provides the meaning of an unfamiliar word, which is literally hidden in plain sight in a literary work such as a paragraph, essay, articles, or passage.

In this context, "rigidly fixed" is a context clue which best helps readers to determine the meaning of the word standard because it is not dynamic but static.

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Answer:

B. "rigidly fixed"

Explanation:

theres no other option

What moves toward the east during el niño? warm water cold water slow currents fast currents

Answers

Answer:

El Nino is a climate change pattern that describes the unusual warming of the water of the Pacific Ocean. The atmospheric pressure above the water decreases. The warm water increases the temperature of the wind. The warm wind moves towards the East Equator.

Explanation:

Answer:

a

Explanation:

warm water

Acids increase the concentration of hydronium ions in solution by donating hydrogen ions to water molecules. true false

Answers

The statement about Acids increasing the concentration of hydronium ions in solution is; True

What is the concentration of the solution?

In pure water and in neutral solutions, we know that the Hydroxonium ions [H₃O⁺] and Hydroxyl Ions [OH⁻] are equal. Therefore, [H₃O⁺] = [OH⁻] = 1 * 10⁻⁷.

However, that concentration can be altered by the addition of an acid or abase. Thus, If an acid is added to pure water the concentration of hydronium ions in the solution will increase.

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Answer:

True

Explanation:

I took the test and it was right.

Chlamydia can increase a woman's risk for developing __________.

Answers

Answer:

cervical cancer :)

Have an amazing day!!

Please rtae and mark brainliest!

Heterotrophs obtain energy from all of the following except

Answers

the answer is solar radiation.

At what temperature teq do the forward and reverse corrosion reactions occur in equilibrium?

Answers

Standard Gibb's free energy at 298K and 5975K is 3.16×10⁶J and -3.83×10⁵J respectively, and temperature at equilibrium state is 5362.3 K.

What is the standard Gibb's free energy?

The complete question is in the brainly link at the end. We can say that;

Standard Gibb's free energy of any reaction is gotten from the formula;

∆G° = ∆H° - T∆S°

where;

∆G° is change in free energy

∆H° is change in enthalpy = 3352 kJ = 3352 × 10³J

∆S° is change in entropy = 625.1 J/K

T is absolute temperature = 298 K

Plugging in the relevant values into the gibbs energy equation gives;

∆G° = (3352 × 10³) - (298 × 625.1)

∆G° = 3.16 × 10⁶J

Gibb's free energy at temperature of 5,975 K is;

∆G° = (3,352 × 10³) - (5,975 × 625.1)

∆G° = -3.83 × 10⁵J

At the equilibrium state, the value of Gibb's free energy is zero. Thus we can calculate the temperature as;

0 = (3352 × 10³)J - (T × 625.1 J/K)

Solving for T gives;

T = 5362.3 K

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Which type of stoichiometric calculation does not involve the gram formula mass

Answers

A type of stoichiometric calculation that doesn't involve the use of gram formula mass is volume-volume problem.

What is a stoichiometric calculation?

A stoichiometric calculation can be defined as a type of calculation which is typically used to measure the quantitative relationships that exists between two or or more chemical compounds that are undergoing a chemical reaction.

This ultimately implies that, a stoichiometric calculation is generally used to study the quantities of reactants and products of two or or more chemical compounds before, during, and after a chemical reaction.

In this scenario, volume-volume problem is a type of stoichiometric calculation that doesn't involve the use of gram formula mass.

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What can the reader infer from the following statement? ""so he finally broke. so even dally has a breaking point.""

Answers

Even the toughest people have breaking points. Is this when I saw the name dally, is it talking about the outsiders?

A random sample of 20 students yielded a mean of x 72

Answers

Answer:

1440

Explanation:

What does the underlined figurative language on page 3 help the reader understand about frost?

Answers

Answer:

frost endured a number of hardships during his lifetime.

Explanation:

I did the thing

Frost faced many challenges throughout his life is the underlined figurative language on page 3 help the reader understand about frost.

What is frost?

Water that has changed from a liquid or gas to a solid is called frost. Typically, frost forms on exterior objects like cars, windows, and plants when there is moist air present. Areas with a lot of fog frequently have heavy frosts. Frost develops when an outside surface cools below the dew point.

Temperatures higher than 32 °F can cause frost to occur. A1: The ice coating that forms on surfaces at or below 32 degrees Fahrenheit is what is referred to as frost. On occasion, frost can develop over night on your grass even though the temperature has not fallen below freezing.

When water vapour from an environment above freezing comes into touch with a solid surface, a thin film of ice called "frost" is created.

Thus, Frost faced many challenges throughout his life.

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Who, in the scary fairy tale, will be happy that goldilocks found jack and jill? goldilock's boss their mom the tree bears the vegetables

Answers

Based on the scary fairy tale, Jack and Jill's mom would be the happiest that are children were found by goldilocks.

What is a fairy tale?

A fairy tale is also referred to as a fictional story and it can be defined as an imaginative literary work (story) that is often narrated and shown in a variety of media to children, especially through the use of fanciful, magical, and wondrous characters such as goldilocks, goblins, elves, etc.

Based on the scary fairy tale, Jack and Jill's mom would be the happiest that are children were found by goldilocks because she was really saddened by the news of their disappearance.

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Ddt is a synthetic compound commonly used as an insecticide and in the 20th century, was used to control mosquito species that commonly spread diseases like malaria. the data illustrates the percent resistance for three species of mosquitoes over three decades. contrast this data to the steps of natural selection and explain the trend seen here.

Answers

Answer:

D

Explanation:

In which of these areas would you expect to find the largest population of rabbits

Answers

in which of what areas? i’m not seeing where you put any answer choices

Dr. roberts conducts a study in which one group of participants counts the number of syllables in each member of a list of twenty words, and the second group creates stories from the same set of words. when later asked to write down as many of the previously seen words as possible, the second group of participants recalls more words than the first group. this study shows the importance of the pragmatics of language the pragmatics of language semantic encoding semantic encoding maintenance rehearsal maintenance rehearsal convergent thinking convergent thinking shallow processing

Answers

semantic encoding

siuuu

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