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

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1 Answer
Mar 2, 2018

#(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)#