MathCastle
Counting & ProbabilityChallengeBinomial Theorem, Pascal & Combinatorial Identities

Binomial Theorem, Pascal & Combinatorial Identities · Challenge problem

Evaluate ∑k=1n(−1)k−1k(nk)\displaystyle\sum_{k=1}^{n}(-1)^{k-1}k\binom{n}{k} for n≥2n\ge 2.