1*2C(1,n)+2*2C(2,n)+3*2C(3,n)+.+n*2C(n,n)求和
1*2C(1,n)+2*2C(2,n)+3*2C(3,n)+.+n*2C(n,n)求和
數(shù)學(xué)人氣：358 ℃時間：2020-09-30 23:56:49
優(yōu)質(zhì)解答
i*C(n,i)=i*n!/[i!(n-i)!]=n!/[(i-1)!(n-i)!]=n*(n-1)!/[(i-1)!(n-i)!]=n*C(n-1,i-1)所以∑(1_n)i*C(n,i)=∑(1_n)n*C(n-1,i-1)=n∑(1_n)C(n-1,i-1)=n∑(0_n-1)C(n-1,i)=n*2^(n-1).也就是1*C(n,1)+2*C(n,2)+3*C(n,3)+...
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