# Solve the following

Question:

If S1 and S2 denote respectively the sum of first 100 natural numbers and the sum of their cubes, then the relation between S1 and S2 is __________.

Solution:

Let

S1 : the sum of first 100 natural numbers

S2 : the sum of their cubes.

$S_{1}=\frac{n(n+1)}{2}=\frac{100(100+1)}{2}$

$S_{1}=5050$

$S_{2}=\left(\frac{n(n+1)}{2}\right)^{2}$

$=\left(\frac{100(100+1)}{2}\right)^{2}$

$=(5050)^{2}$

$S_{2}=S_{1}^{2}$