Đáp án: `A=1/2-1/(2.3^99)`
Giải thích các bước giải:
`A=1/3+1/3^2+1/3^3+1/3^4+....+1/3^98+1/3^99`
`3A=1+1/3+1/3^2+1/3^3+....+1/3^97+1/3^98`
`2A=3A-A=(1+1/3+1/3^2+1/3^3+....+1/3^97+1/3^98)-(1/3+1/3^2+1/3^3+1/3^4+....+1/3^98+1/3^99)`
`2A=1-1/3^99`
$A=\dfrac{2A}{2}=\dfrac{1-\dfrac{1}{3^{99}}}{2}$
`A=1/2-1/(2.3^99)`
Vậy `A=1/2-1/(2.3^99)`