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What is a formula to calculate the sum of the first n positive integers? Could you explain why this formula works?

Question

What is a formula to calculate the sum of the first n positive integers? Could you explain why this formula works?

check_circleAnswer
Step 1

Obtain the sum of first n positive integers as follows.

The general formula to calculate the sum of first n positive integer is,

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Step 2

The given sequence of n integers represents an arithmetic sequence.

If the difference between any two consecutive terms in a sequence is same, then the sequence is called as an Arithmetic sequence.

The formula to find the sum of first n terms in an arithmetic sequence is,

 

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Step 3

For the first n positive integers, the difference between any two terms is 1.

That is, the common difference is 1.

Also, the first positive int...

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