Problem A. 671. (May 2016)

A. 671. Prove that

\(\displaystyle 0< \sum_{i=0}^k {(-1)}^{i}\binom{n+1}{i}{(k+1-i)}^n < n! \)

holds for every pair \(\displaystyle 0<k<n\) of integers.

(5 pont)

Deadline expired on June 10, 2016.

Statistics:

7 students sent a solution.
5 points:	Baran Zsuzsanna, Bodnár Levente, Polgár Márton, Williams Kada.
2 points:	3 students.

Problems in Mathematics of KöMaL, May 2016