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Prove by mathematical induction that (1)...

Prove by mathematical induction that `(1)/(1+x)+(2)/(1+x^2)+(4)/(1+x^4)+.....+(2^n)/(1+x^(2^n))=(1)/(x-1)+(2^(n+1))/(1-x^(2^(n+1)))` where , `|x|ne 1 ` and n is non - negative integer.

Text Solution

Verified by Experts

Let`P(n):(1)/(1+x)+(2)/(1+x^2)+(4)/(1+x^4)+.....+(2^n)/(1+x^(2^(n)))`
`=(1)/(x-1)+(2^(n+1))/(1-x^(2^(n+1)))` .....(i)
Step I For `n=1`,
LHS of Eq. (i) =(1)/(1+x)+(2)/(1+x^2)`
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