Find sum of the series - 2

I will give $2$ solutions

First solution

It will be easy if you know calculus

$s-1≤∫_{1}^{100}x^{-1/3}dx≤s$ $s-1≤∫_{1}^{100}\frac{d\frac{3}{2}x^{\frac{2}{3}}}{\cancel{dx}}\cancel{dx}≤s$ $s-1≤∫_{1}^{100}d\frac{3}{2}x^{\frac{2}{3}}≤s$ $s-1≤\frac{3}{2}\sqrt{100^2}-\frac{3}{2}\sqrt{1^2}=\frac{3}{2}(\sqrt{100^2}-1)=30.8165204...≤s$ $s\approx31$

Second solution

Through the coding environment in Brilliant: