Write the formula for the sum of first $n$ positive integers.

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Solution

First $n$ positive integers are $1, 2, . . ., n .$ \
They are in A.P. with $a = 1, d = 1$
Sum will be $1 + 2 + . . . + n = \frac{n}{2} [2 a + (n - 1) d]$
$= \frac{n}{2} [2 (1) + (n - 1) 1]$
$= \frac{n}{2} [2 + n - 1]$
$= \frac{n (n + 1)}{2}$

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Write the formula for the sum of first n positive integers.

First n positive integers are 1,2,...,n.\They are in A.P. with a=1,d=1Sum will be 1+2+...+n=n2[2a+(n−1)d]=n2[2(1)+(n−1)1]=n2[2+n−1]=n(n+1)2

Write the formula for the sum of first $n$ positive integers.

First $n$ positive integers are $1, 2, . . ., n .$ \
They are in A.P. with $a = 1, d = 1$
Sum will be $1 + 2 + . . . + n = \frac{n}{2} [2 a + (n - 1) d]$
$= \frac{n}{2} [2 (1) + (n - 1) 1]$
$= \frac{n}{2} [2 + n - 1]$
$= \frac{n (n + 1)}{2}$