`C= 1/3 - 2/3^2 + 3/3^3 - 4/3^4+...+99/3^99 - 100/3^100`
`3C= 3(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 = 1-2/3 + 3/3^2 - 4/3^3 +...+99/3^98 - 100/3^99 +1/3 - 2/3^2 + 3/3^3 - 5/3^4 +...+99/3^99 - 100/3^100`
`4C= 1- 1/3 + 1/3^2 - 1/3^3+....+1/3^98 - 1/3^99`
Đặt `A= 1 - 1/3 + 1/3^2 -1/3^3+...-1/3^99`
`1/3 A = 1/3( 1 - 1/3 + 1/3^2 -1/3^3+...-1/3^99)`
`1/3A = 1/3 - 1/3^2 + 1/3^3-....-1/3^100`
`A+ 1/3 A = 1 - 1/3 + 1/3^2 -1/3^3+...+1/3^98 - 1/3^99 + 1/3 -1/3^2 + 1/3^3 -....-1/3^100`
`4/3 A= 1- 1/3^100`
`A = (1-1/3^100) :4/3`
`A= 3/4 - 1/(3^99. 4)`
`=> 4C = (3/4 - 1/(3^99. 4))`
`=> C = (3/4 - 1/(3^99.4)) : 4`
`C= (3/4 - 1/(3^99. 4)) . 1/4`
`C= 3/16 - 1/(3^99. 16) < 3/16`
Vậy `C < 3/16`
