Sn=1*1/2+2*1/4+3*1/8+...+n*1/2^n,错位相减求和!

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Sn=1*1/2+2*1/4+3*1/8+...+n*1/2^n,错位相减求和!

Sn=1*1/2+2*1/4+3*1/8+...+n*1/2^n,错位相减求和!
Sn=1*1/2+2*1/4+3*1/8+...+n*1/2^n,错位相减求和!

Sn=1*1/2+2*1/4+3*1/8+...+n*1/2^n,错位相减求和!
1/2Sn=1*1/4+2*1/8+……+(n-1)*1/2^n+n*1/2^(n+1)
Sn=2(Sn-1/2Sn)=2(1*1/2+(1/4+1/8+……+1/2^n)-n*1/2^(n+1))
=2(1/2-n*1/2^(n+1)+(1/4+1/8+……1/2^n))
=2(1/2-n/2^(n+1)+((1/4-1/2^n)/(1-1/2(n-2)))

思路:Sn-1/2Sn=1/2+1/4+1/8+...+1/2^(n-1)+n*1/2^n-n*1/2^(n+1)