Đáp án:
Giải thích các bước giải:
`A=1/3+2/3^2+3/3^3+4/3^4+...+100/3^100+101/3^101`
`=>3A=3.(1/3+2/3^2+3/3^3+4/3^4+...+100/3^100+101/3^101)`
`=>3A=1+2/3+3/3^2+4/3^3+...+100/3^99+101/3^100`
`=>3A-A=(1+2/3+3/3^2+4/3^3+...+100/3^99+101/3^100)-(1/3+2/3^2+3/3^3+4/3^4+...+100/3^100+101/3^101)`
`=>2A=1+1/3+1/3^2+1/3^3+...+1/3^100+100/3^101`
`=>6A=3.(1+1/3+1/3^2+1/3^3+...+1/3^100+100/3^101)`
`=>6A=3+1+1/3+1/3^2+...+1/3^99+100/(3^100)`
`=>6A-2A=(3+1+1/3+1/3^2+...+1/3^99+100/(3^100))-(1+1/3+1/3^2+1/3^3+...+1/3^100+100/3^101)`
`=>4A=3+100/3^100-100/3^101`
`=>`$A=\dfrac{3+\dfrac{100}{3^{100}}-\dfrac{101}{3^{101}}}{4}$
`=>`$A=\dfrac{3}{4}+\dfrac{\dfrac{100}{3^{100}}-\dfrac{101}{3^{101}}}{4}<\dfrac34$
Vậy `A<3/4`.
