Question

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

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,

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,

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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