Đặt `A=5/2 +9/4 +17/8 +33/16+129/64+257/128+513/256+1025/512+2049/1024`

`=5/2 +9/2^2 +17/2^3 +33/2^4+129/2^6+257/2^7+513/2^8+1025/2^9+2049/2^10`

`=(2+1/2)+(2+1/4)+...+(2+1/1024)`

`=(2+2+...+2)+(1/2+1/4+...+1/1024)-1/32`  

`=2xx9+(1/2+1/2^2+...+1/2^10)-1/2^5`  

Đặt `B=1/2+1/2^2+...+1/2^10`

`2B=1+1/2+...+1/2^9`

`2B-B=(1+1/2+...+1/2^9)-(1/2+1/2^2+...+1/2^10)`

`B=1+(1/2-1/2)+...+(1/2^9-1/2^9)-1/2^10`

`B=1-1/1024`

`B=1023/1024`

Thay `B` vào `A` ta được : 

`A=18+1023/1024-1/32`

`=18432/1024+1023/1024-32/1024`

`=19423/1024`

Vậy `5/2 +9/4 +17/8 +33/16+129/64+257/128+513/256+1025/512+2049/1024=19423/1024`