`1/(x+1)-2/(x^4-x+1)<(1-2x)/(x^3+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)

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 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)

Solve the inequality,(1)/(x-1)-(4)/(x-2)+(4)/(x-3)-(1)/(x-4)<(1)/(30)

Without expanding, find the value of: (i) (x + 1)^4 - 4(x + 1)^3 (x - 1) + 6(x + 1)^2 (x - 1)^2 - 4(x + 1) (x - 1)^3 + (x -1)^4 (ii) (2x - 1)^4 + 4(2x - 1)^3 (3 - 2x) + 6(2x - 1)^2 (3 - 2x)^2 + 4(2x - 1) (3 - 2x)^3 + (3 - 2x)^4

Consider the function g(x) defined as g(x) (x^(2011-1)-1)=(x+1)(x^2+1)(x^4+1)...(x^(2^(2010))+1)-1 . Then the value of g(2) is equal to

Consider the function g(x) defined as g(x)(x^(2011-1)-1)=(x+1)(x^(2)+1)(x^(4)+1)...(x^(2^(2010))+1)-1 Then the value of g(2) is equal to

Express 1/(1-x)+1/(1+x)+2/(1+x^2)+4/(1+x^4) as a rational expression: