Tính nhanh: M= 1 - 1/2 -1/4-1/8-1/16-1/32-...-1/1024-1/2048

Đáp án `+` Giải thích các bước giải:

`M=1-1/2-1/4-1/8-1/16-1/32-...-1/1024-1/2048`

`M=1-(1/2+1/4+1/8+1/6+1/32+...+1/1024+1/2048)`

Ta tính `1/2+1/4+1/8+1/16+1/32+...+1/1024+1/2048` như sau:

Đặt `S=1/2+1/4+1/8+1/16+1/32+...+1/1024+1/2048`

`2×S=2xx(1/2+1/4+1/8+1/16+1/32+...+1/1024+1/2048)`

`2×S=1+1/2+1/4+1/8+1/16+1/32+...+1/1024`

`2×S-S=(1+1/2+1/4+1/8+1/16+1/32+...+1/1024)-(1/2+1/4+1/8+1/16+1/32+...+1/1024+1/2048)`

`S=1-1/2048`

`S=2047/2048`

Thay vào ta có:

`M=1-(1/2+1/4+1/8+1/6+1/32+...+1/1024+1/2048)`

`M=1-2047/2048`

`M=1/2048.`

Vậy `M=1/2048.`

`#Ph.`