1. Tính nhanh: a, 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256 b, 1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729 c, 1 + 5/4 + 5/8 + 5/16 + 5/32 + 5/64 Cần giải ra đầy đủ, dễ hiểu ạ

`a,` 

Đặt: 

`A = 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256`

`A xx  2 = 2 xx (1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256)`

`A xx 2 = 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128`

`A xx 2 - A = (1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128) - (1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256)`

`A = 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256 - 1/2 - 1/4 - 1/8 - 1/16 - 1/32 - 1/64 - 1/128 - 1/256`

`A = 1 - 1/256`

`A = 255/256`

`b,`

Đặt:

`B = 1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729`

`3 xx B = 3 . (1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729)`

`3 xx B = 1 + 1/3 + 1/9 + 1/27 + 1/81 + 1/243`

`3 xx B - B = (1 + 1/3 + 1/9 + 1/27 + 1/81 + 1/243) - (1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729)`

`2 xx B = 1 + 1/3 + 1/9 + 1/27 + 1/81 + 1/243 - 1/3 - 1/9 - 1/27 - 1/81 - 1/243 - 1/729`

`2 xx B = 1 - 1/729`

`2 xx B = 278/279`

`B = 278/279 : 2`

`B = 364/279`

`c,` 

Đặt:

`C = 1 + 5/4 + 5/8 + 5/16 + 5/32 + 5/64`

`C = 5 xx (1/5 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64)`

Đặt:

`D = 1/5 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64`

`2 xx D = 2 xx (1/5 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64)`

`2 xx D = 2/5 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32`

`2 xx D - D = (2/5 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32) - (1/5 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64)`

`D = 2/5 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 - 1/5 - 1/4 - 1/8 - 1/16 - 1/32 - 1/64`

`D = 2/5 + 1/2 - 1/5 - 1/64`

`D = 1/5 + 1/2 - 1/64`

`D = 1/5 + 63/64`

`->` `C = 5 xx (1/5 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64)`

`C = 5 xx (1/5 + 63/64)`

`C  = 1 + 315/64`

`C = 1 315/64`