已知数列{an},an=n(1/2)^n,求S10

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已知数列{an},an=n(1/2)^n,求S10
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已知数列{an},an=n(1/2)^n,求S10
已知数列{an},an=n(1/2)^n,求S10

已知数列{an},an=n(1/2)^n,求S10
因为 S10=1/2+2*(1/2)^2+3*(1/2)^3+.+10*(1/2)^10 ,
因此 2*S10=1+2*(1/2)+3*(1/2)^2+4*(1/2)^3+.+9*(1/2)^8+10*(1/2)^9 ,
两式相减得 S10=1+1/2+(1/2)^2+.+(1/2)^9-10*(1/2)^10=2-(1/2)^9-10*(1/2)^10=2-3*(1/2)^8 ,
即 S10=509/256 .