Rút gọn: A=1/2+1/2^2+1/2^3+...+1^2^100

Đáp án:

`A=(2^100-1)/(2^100)`

Trình bày lời giải:

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