Đáp án:
Giải thích các bước giải:
`C = 1/3 - 2/3^2 + 3/3^3 - 4/3^4 + .... + 99/3^{99} - 100/3^{100}`
`=>3C=1 -2/3 + 3/(3^2) - 4/(3^3) +...+99/(3^98) -100/(3^99)`
`=>3C+C=1-1/3+1/3^2-1/3^3+1/3^4-...+1/3^98-1/3^99-100/3^100`
`=>4C=1-1/3+1/3^2-1/3^3+1/3^4-...+1/3^98-1/3^99-100/3^100`
Đặt `B=1-1/3+1/3^2-1/3^3+1/3^4-...+1/3^98-1/3^99`
`=>3B=3 -1 +1/3 -1/(3^2) +1/(3^3)+...+1/(3^97) -1/(3^98)`
`=>3B+B=3-1/(3^99)`
`=>B=3/4 - 1/(3^99 .4)`
`=>4C=3/4 - 1/(3^99 .4)-100/(3^100)`
`=>4C<3/4`
`=>C<3/16`
