Gauss Trick in ISI Entrance
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
From I.S.I. Entrance and erstwhile Soviet Olympiad.
Test of Mathematics at 10+2 Level by East West Press, Subjective Problem 31
Challenges and Thrills of Pre College Mathematics
Try the first hint
Other useful links:-
- https://cheenta.com/complex-number-isi-entrance-b-stat-hons-2003-problem-5/
- https://www.youtube.com/watch?v=P4ZYA4XCQoM&list=PLTDTcDkWcXuxeaAMvWpx4vGIul38dKOQp&index=4