Đáp án:
`A<1/4`
Giải thích các bước giải:
`A=1/3^2+1/3^3+1/3^4+...+1/3^101`
`=>3A=3(1/3^2+1/3^3+1/3^4+...+1/3^101)`
`=>3A=1/3+1/3^2+1/3^3+...+1/3^100`
`=>3A-A=(1/3+1/3^2+1/3^3+...+1/3^100)-(1/3^2+1/3^3+1/3^4+...+1/3^101)`
`=>2A=1/3-1/3^101`
`=>`$A=\dfrac{\dfrac{1}{3}-\dfrac{1}{3^{101}}}{2}$
`=>A=1/6-1/2.3^101`
`=>A<1/6<1/4`
Vậy `A<1/4`.