Some sums

Algebra Level 2

$\large 1^3 + 2^3 + \cdots + 2016^3 - (1 + 2 + \cdots + 2016)^2 = \, ?$

3 solutions

Goh Choon Aik
Apr 14, 2016

tbh I guessed

This is not a solution - please refrain from posting in the solutions section if you have nothing to share.

Michael Fuller - 5 years, 2 months ago

Atul Shivam
Apr 12, 2016

Let $1^3+2^3+3^3+4^3+...+2016^3=(\frac{2016×2017}{2})^2.........(1)$

Now $(1+2+3+4+....+2016)^2= (\frac{2016×2017}{2})^2.........(2)$ since both $(1),(2)$ are same so $(1)-(2)=0$

A Former Brilliant Member
Apr 12, 2016

$1^3 + 2^3 + \cdots + 2016^3 - (1 + 2 + \cdots + 2016)^2$

$=(1 + 2 + \cdots + 2016)^2-(1 + 2 + \cdots + 2016)^2$

$=\boxed0$ .