Question
Prove that $$\sum_{k=0}^{m}(-1)^{k} C(n, k)=(-1)^{m} C(n-1, m)$$ for all $m, 0 \leq m \leq n-1$
Step 1
This can be written as: \[ \sum_{k=0}^{m}(-1)^{k} C(n, k) = C(n, 0) - C(n, 1) + C(n, 2) - C(n, 3) + \ldots + (-1)^{m} C(n, m) \] Show more…
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