Question

What is the following simplified? Thanks in advance for the answer.

Answer 1

`(2^{2^50}-1)`

Explanation:

Multiply both sides of the equation by `(2-1)`

`(2-1)S = (2-1) times {(2+1)(2^2+1)(2^{2^2)+1)(2^{2^3)+1)...(2^{2^49)+1)}`
`= (2-1) times (2+1)times {(2^2+1)(2^{2^2)+1)(2^{2^3)+1)...(2^{2^49)+1)}`
`=(2^2-1)times {(2^2+1)(2^{2^2)+1)(2^{2^3)+1)...(2^{2^49)+1)}`
`= (2^{2^2}-1) times {(2^{2^2)+1)(2^{2^3)+1)...(2^{2^49)+1)}`
...
`=(2^{2^49)-1) times (2^{2^49}+1) = (2^{2^50}-1)`