Question

What is the difference between the sum of first n odd natural numbers and that of first n natural numbers?

Answer 1

$i ) Sum \:of \: first \:n \:odd \\natural \: numbers = n^{2} \: ---(1)$

$ii ) Sum \:of \: first \:n \:natural \: numbers \\= \frac{n(n+1)}{2} \: ---(2)$

/* According to the problem given */

The difference between the sum of first n odd natural numbers and that of first n natural numbers $= n^{2} - \frac{n(n+1)}{2}\\= n^{2} - \frac{n^{2}+n}{2} \\= \frac{2n^{2} - (n^{2}+n)}{2} \\= \frac{2n^{2} - n^{2} - n}{2} \\= \frac{n^{2} - n}{2}$

Therefore.,

$\red { Required \: Difference }\green {= \frac{n^{2} - n}{2}}$

•••♪