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lesya692 [45]
2 years ago
12

1 (15 Points]. Prove the following statement: is divisible by 3 if only if it is a sum of three consecutive integers. be ddvisbk

Mathematics
1 answer:
Alinara [238K]2 years ago
4 0

Answer:

<em>First.</em> Let us prove that the sum of three consecutive integers is divisible by 3.

Three consecutive integers can be written as k, k+1, k+2. Then, if we denote their sum as n:

n = k+(k+1)+(k+2) = 3k+3 = 3(k+1).

So, n can be written as 3 times another integer, thus n is divisible by 3.

<em>Second. </em>Let us prove that any number divisible by 3 can be written as the sum of three consecutive integers.

Assume that n is divisible by 3. The above proof suggest that we write it as

n=3(k+1)=3k+3=k + k + k +1+2 = k + (k+1) + (k+2).

As k, k+1, k+2 are three consecutive integers, we have completed our goal.

Step-by-step explanation:

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Which is the range of the function f(x) = (9)×?
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Using it's concept, it is found that the range of the function f(x) = 9^x is given by:

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<h3>What is the range of a function?</h3>

It is the set that contains all possible output values for the function.

In this problem, the function is:

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For <u>exponential functions without vertical shifts</u>, as is the case in this problem, the range is given by:

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More can be learned about the range of a function at brainly.com/question/10891721

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