tính A biết : A= 1 + 1/3 - 1/3^2 + 1/3^3 - 1/3^4 + ... + 1/3^199 - 1/3^200

Đáp án:

 `A = (5-1/(3^200))/4`

Giải thích các bước giải:

 `A = 1 + 1/3 - 1/(3^2) + 1/(3^3) - 1/(3^4) +...+ 1/(3^199) - 1/(3^200)`

`3A = 3 + 1 - 1/3 + 1/(3^2) - 1/(3^3) +...+ 1/(3^198) - 1/(3^199)`

`=> A + 3A = (1 + 1/3 - 1/(3^2) + 1/(3^3) - 1/(3^4) +...+ 1/(3^199) - 1/(3^200) + (3 + 1 - 1/3 + 1/(3^2) - 1/(3^3) +...+ 1/(3^198) - 1/(3^199) )`

`=> 4A = 1 + 1/3 - 1/(3^2) + 1/(3^3) - 1/(3^4) +...+ 1/(3^199) - 1/(3^200) + 3 + 1 - 1/3 + 1/(3^2) - 1/(3^3) +...+ 1/(3^198) - 1/(3^199)`

`=> 4A = (1+ 3 + 1) + (1/3 - 1/3) -   (1/(3^2) - 1/(3^2) ) +(1/(3^3) - 1/(3^3) ) - ( 1/(3^4) - 1/(3^4) ) + ...+ (1/(3^198) - 1/(3^198) ) +   (1/(3^199) - 1/(3^199) ) - 1/(3^200)`

`=> 4A = 5 - 1/(3^200) `

`=> A = (5-1/(3^200))/4`

 Vậy `A = (5-1/(3^200))/4`