Question

2/2+3/4+4/8+5/16+…+11/1024等于多少?

Answer 1

需要用到高中等比列求和

设 S = 2/2+3/4+4/8+5/16+...+10/2^9+11/2^10

2S = 2 + 3/2+4/4+5/8+……+ 11/2^9

下式-上式得：

S = 2 + 1/2 +1/4+……+1/2^9 - 11/2^10

= 2 + 1/2 (1- 1/2^9) / (1-1/2) - 11/2^10

= 2+ 1 - 1/2^9 - 11/2^10

= 3 - 13/2^10

= 3 - 13 / 1024