Giải nhanh giúp mình

Đáp án:

`A = 511/512` 

Giải thích các bước giải:

Cách  `1:`

`A = 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256 + 1/512`

`A = 1/2^2 + 1/2^3 + 1/2^4 + 1/2^5 + 1/2^6 + 1/2^7 + 1/2^8 + 1/2^9`

`2A = 1/2 + 1/2^2 + 1/2^3 + 1/2^4 + 1/2^5 + 1/2^6 + 1/2^7 + 1/2^8`

`2A - A = ( 1/2 + 1/2^2 + 1/2^3 + 1/2^4 + 1/2^5 + 1/2^6 + 1/2^7 + 1/2^8 )`

`- ( 1/2^2 + 1/2^3 + 1/2^4 + 1/2^5 + 1/2^6 + 1/2^7 + 1/2^8 + 1/2^9 )`

`A = 1/2 - 1/2^9`

`A = 1/2 - 1/512`

`A = 256/512 - 1/512`

`A = 255/512`

Cách  `2:`

`A = 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256 + 1/512`

`A = 128/512 + 64/512 + 32/512 + 16/512 + 8/512 + 4/512 + 2/512 + 1/512`

`A = ( 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 )/512`

`A = 255/512`