Giải thích các bước giải:
`H=1+2.3+3.3^2+4.3^3+...+101.3^100`
`2H=101.3^101-(3^100+3^99+3^98+...+3)-1(1)`
Đặt:
`N=3^100+3^99+3^98+...+3`
`3N=3^101+3^100+...+3^2`
`3N-N=(3^101+3^100+...+3^2)-(3^100+3^99+3^98+...+3)`
`2N=3^101-3`
`N=[3^101-3]/2`
Thay N vào (1) ta có:
`2H=101.3^101-[3^101-3]/2-1`
`H=[101.3^101-[3^101-3]/2-1]/2`
`H=[3^101. 201-1]/2. 1/2`
`H=[3^101. 201-1]/4`