Obtain the sum of `1/(x+1)+2/(x^2+1)+4/(x^4+1)+......+(2^n)/(x^(2^n)+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.

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.

Show that 1/(x+1)+2/(x^2+1)+4/(x^4+1)+…..+2^n/(x^(2n+1))=1 /(x-1)- 2^(n+1)/(x^(2^(n+1)) -1)

Show that 1/(x+1)+2/(x^2+1)+4/(x^4+1)+…..+2^n/(x^(2n)+1)=1 /(x-1)- 2^(n+1)/(x^(2^(n+1)) -1)

Show that 1/(x+1)+2/(x^2+1)+4/x^4+1)+…..+2^n/(x^2^n+1)= /(x-1)- 2^(n+1)/(x^2(n+1) -1)

Show that 1/(x+1)+5/(x^2+1)+4/x^4+1)+…..+2^n/(x^2^n+1)= /(x-1)- 2^(n+1)/(x^2(n+1) -1)

if |x| oo)(1+x)(1+x^2)(1+x^4)........(1+x^(2n))=

The sum of : (x+ 2)^(n-1) + ( x+2) ^(n-2) (x+1) + ( x+2)^(n-3) (x+1)^(2) + "......." + ( x+ 1)^(n-1) equals :

The sum of (x+2)^(n-1)+ (x+2)^(n-2) (x+1) + (x+2)^(n-3) (x+1)^(2) + cdots + (x+1)^(n-1) is equal to

(1)/(2) tan"" ((x)/(2) ) + (1)/( 4) (tan"" (x)/(4) ) + ...... + (1)/(2^(n) ) tan"" ((x)/( 2^n) ) =