求满足不等式C(n,1)+2C(n,2)+……+nC(n,n)

问题描述:

求满足不等式C(n,1)+2C(n,2)+……+nC(n,n)

因为2^n=C(n,0)+C(n,1)+2C(n,2)+……+nC(n,n)
所以C(n,1)+2C(n,2)+……+nC(n,n)=2^n-C(n,0)=2^n-1使2^n-1

我们先来求和,令S=C(n,1)+2C(n,2)+……+nC(n,n)
首先,
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