Cho `A = 1/2+2/2^2+3/2^3+...+100/2^100 `
`A = 1/2+2/2^2+3/2^3+...+100/2^100 `
`2A = 1+1+3/2^2+...+100/2^99`
`2A-A = (1+1+3/2^2+...+100/2^99)-(1/2+2/2^2+3/2^3+...+100/2^100)`
`A = 1+ 1/2 + 1/2^2+ ...+ 1/2^99 - 100/2^100`
Cho `B = 1+ 1/2 + 1/2^2+ ...+ 1/2^99`
`2B = 2+1 + 1/2^2 + ...+1/2^98`
`2B-B = (2+1 + 1/2^2 + ...+1/2^98)-(1+ 1/2 + 1/2^2+ ...+ 1/2^99)`
`B = 2 - 1/2^99`
Vậy `A = 2 - 1/2^99 - 100/2^100 < 2`
