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binomial inequality, with pairs of nonnegative integers

Source: Irmo 2015 p2 q10

September 16, 2018
BinomialinequalitiesBinomial summationInequality

Problem Statement

Prove that, for all pairs of nonnegative integers, j,nj,n, ∑K=0nkj(nk)≥2n−jnj\sum_{K=0}^{n}k^j\binom n k \ge 2^{n-j} n^j
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