Question

The natural numbers are written in the form of a triangle as shown below :
The sum of numbers in all the n rows .

Answer 1

All the numbers are natural numbers and if N be their number, then
N = 1 + 2 + 3 + 4 + .... $n=\frac{n(n+1)}{2}$
$\therefore S_n=\frac{N(N+1)}{2}=\frac{1}{2}\frac{n(n+1)}{2}[\frac{n(n+1)}{2}+1]$
$=\frac{1}{8}n(n+1)(n^2+n+2)$