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## Problem – Gauss Trick (ISI Entrance)

Let’s learn Gauss Trick for ISI Entrance.

If k is an odd positive integer, prove that for any integer $\mathbf{ n \ge 1 , 1^k + 2^k + \cdots + n^k }$ is divisible by $\mathbf{ \frac {n(n+1)}{2} }$

### Key Concepts

Gauss Trick

Factoring Binomial

## Source

But try the problem first…

From I.S.I. Entrance and erstwhile Soviet Olympiad.

Source

Test of Mathematics at 10+2 Level by East West Press, Subjective Problem 31

Challenges and Thrills of Pre College Mathematics