## Trending News

Promoted

# ∑k(k-1)C(n,k) using the binomial theorem and some calculus, evaluate?

∑k(k-1)C(n,k) using the binomial theorem and some calculus, evaluate

### 1 Answer

Relevance

- kbLv 71 decade agoFavorite Answer
By the Binomial Theorem,

(1 + x)^n = sum(k=0 to n) C(n,k) x^k.

Differentiating both sides twice, we get

n(n - 1) (1 + x)^(n - 2) = sum(k=2 to n) k(k - 1) C(n,k) x^(k - 2).

Now, set x = 1:

n(n - 1) 2^(n - 2) = sum(k=2 to n) k(k - 1) C(n,k).

I hope this helps!

Still have questions? Get your answers by asking now.