1/2+3/2^2+5/2^3……+2n-1/2^n.n趋向无穷大

问题描述:

1/2+3/2^2+5/2^3……+2n-1/2^n.n趋向无穷大

设S=1/2+3/2²+5/2³+…+(2n-1)/(2^n),则:
(1/2)S=1/2²+3/2³+…+(2n-1)/[2^(n+1)]
两式相减,得:
得:(1/2)S=(3/2)-(2n+3)/[2^(n+1)],S的极限是3