Let `f(x)=(1-x^(n+1))/(1-x) andg(x)=1-2/x+3/(x^2)-...+(-1)^n(n+1)/(x^n).` Then the constant term in `f prime(x) xx g(x)` is equal to -

Let f(x)=x+(1-x)x^3+(1-x)(1-x^2)x^3+.........+(1-x)(1-x^2)........(1-x^(n-1))x^n;(n >= 4) then :

Let S_(n)(x)=(x^(n-1)+(1)/(x^(n-1)))+2(x^(n-2)+(1)/(x^(n-2)))+"....."+(n-1)(x+(1)/(x))+n , then

Let S_(n)(x)=(x^(n-1)+(1)/(x^(n-1)))+2(x^(n-2)+(1)/(x^(n-2)))+"....."+(n-1)(x+(1)/(x))+n , then

f(x)=(x^(n)-1)/(x-1),x!=1 and f(x)=n^(2),x=1 continuous at x=1 then the value of n

Let f(x) = (x - 1)(x - 2)(x - 3)…(x -n), n in N and f(')(n) = 5040 . Then the value of n is …..

Let f(x)=x+(1-x)x^(3)+(1-x)(1-x^(2))x^(3)+.........+(1-x)(1-x^(2))......*(1-x^(n-1))x^(n);(n>=4) then :

Let f(x)=x+(1-x)x^(2)+(1-x)(1-x^(2))x^(3)+............+(1-x)(1-x^(2)).........(1-x^(n-1))x^(n);(n) then :

Let f(x) =1/x, g(x) = 1/(9x^(2)-1) and h(x) = (11x)/(x+3) be three functions. Let F(x) =(h.g.f)(x) Suppose domain of F is R -{x_(1),x_(2),…….,x_(n)} , where x_(1),x_(2) ,…….. x_(n) are n distinct real numbers. Then n =…………….

Let f(x)=(x)/((1+x^(n))^((1)/(n))) for n>=2 and g(x)=(f(ofo...of)(x) Then int x^(n-2)g(x)dx equals