Give a brief justification for the identity

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

Problem

Give a brief justification for the identity (nk)+(nk+1)=(n+1k+1)\displaystyle {n\choose k}+{n\choose k+1}={n+1\choose k+1}, where nn and kk are positive integers with 0≤k≤n−10\le k\le n-1.

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