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)

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.

cos^(-1)((1-x^(2n))/(1+x^(2n)))

cos^(-1)((1-x^(2n))/(1+x^(2n)))

(x^(2^(n-1))+y^(2^(n-1)))(x^(2^(n-1))-y^(2^(n-1)))=

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

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

Show that: (x)+(x+(1)/(n))+(x+(2)/(n))+...+(x+(n-1)/(n))=nx+(n-1)/(2)