Đáp án:
Giải thích các bước giải:
-Đặt `A = 1/3 - 2/3^2 + 3/3^3 - 4/3^4 +........+ 99/3^99 - 100/3^100`
`=> 3A = 1 - 2/3 + 3/3^2 - 4/3^3 +......+ 99/3^98 - 100/3^99`
`=> 3A + A = 4A = 1 - 1/3 + 1/3^2 - 1/3^3 +.........+ 1/3^98 - 1/3^99 - 100/3^100`
`=> -1/3 . 4A = -1/3 + 1/3^2 - 1/3^3 +........- 1/3^99 + 1/3^100 + 100/3^101`
`=> 4A - 4A . (-1/3) = 1 - ( 101/3^100 + 100/3^101 )`
`=> 4A . ( 1 + 1/3 ) = 1 - ( 101/3^100 + 100/3^101 )`
`=> 4A . 4/3 = A/3 = 1 - ( 101/3^100 + 100/3^101 )`
`=> A = 3 - 3.(101/3^100 + 100/3^101 )`