已知数列{an},an=n(1/2)^n,求S10

问题描述:

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 ,...