>>65
1-p = q と書いて、
Σ[k=0,n]k C[n,k] p^k (1-p)^(n-k)=Σ[k=0,n]k C[n,k] p^k q^(n-k)=p(∂/∂p)Σ[k=0,n] C[n,k] p^k q^(n-k)
= p(∂/∂p)(p+q)^n= np(p+q)^(n-1) = np(p + 1-p)^(n-1) = np.