Explain in at most two sentences why for every positive integer .

MATHEMATICS · Subjective · A Level · Mathematics · Sequences and series · Sequences and series

Problem

Explain in at most two sentences why ∑k=0n(−1)k(nk)=0\displaystyle\sum_{k=0}^{n}(-1)^k{n\choose k}=0 for every positive integer nn.

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