The sum of the series 1/x+1+2/x^2+1+2^2/x^4+1+....2^100/x^2^100 +1 when x = 2 is :

Question

The sum of the series 

\(\cfrac{1}{x+1}\) = \(\cfrac{2}{x^2+1}\) = \(\cfrac{2^2}{x^4+1}\)+.......+\(\cfrac{2^{100}}{x^{2^{100}}+1}\) when x = 2 is :

(1) 1+\(\cfrac{2^{101}}{4^{101}-1}\)

(2)  1+\(\cfrac{2^{100}}{4^{101}-1}\)

(3)  1-\(\cfrac{2^{100}}{4^{100}-1}\)

(4)  1-\(\cfrac{2^{101}}{2^{2^{101}-1}}\)

Answer 1

 Correct answer is: (4)  \(1-\cfrac{2^{101}}{2^{2^{101}-1}}\)