A problem by narendiran veerabhagu

Level pending

What is value of 1+2^3+3^3+...................................99^3+100^3?

1 solution

Mathh Mathh
May 14, 2015

Use $1^3+2^3+\cdots + n^3=\left(\frac{n(n+1)}{2}\right)^2$ .

$\left(\frac{100(101)}{2}\right)^2=5050^2=\boxed{25502500}$ .

Some other formulas: $1+2+\cdots+n=\frac{n(n+1)}{2}$ .

$1^2+2^2+\cdots+n^2=\frac{n(n+1)(2n+1)}{6}$ .

$1^4+2^4+\cdots+n^4=\frac{n(n+1)(2n+1)(3n^2+3n-1)}{30}$ .