求和:3*(1/2)+4*(1/4)+5*(1/8)+...+(n+2)*(1/2^n)

来源：百度知道 编辑：UC知道 时间：2024/05/22 16:21:21

s=3*(1/2)+4*(1/4)+5*(1/8)+...+(n+2)*(1/2^n);.......(1)
2s=2*[3*(1/2)+4*(1/4)+5*(1/8)+...+(n+2)*(1/2^n)]
=3*(1)+4*(1/2)+5*(1/4)+...+(n+2)*(1/2^(n-1)).....(2)
(2)-(1)得:
s=3+(1/2)+(1/4)+(1/8)+...+(1/2^(n-1))-(n+2)*(1/2^n)
=3+1-(1/2^(n-1))-(n+2)*(1/2^n)
=4-(1/2^(n-1))-(n+2)*(1/2^n)

同学啊,老师布置的作业要自己独立完成啊,哎...