(b) If `f(n) = n/(1+n)`then find the value of `f(n) +1/f(n)`

Let f(n)=sum_(k=-n)^(n)(cot^(-1)((1)/(k))-tan^(-1)(k)) such that sum_(n=2)^(10)(f(n)+f(n-1))=a pi then find the value of (a+1) .

If f(n)=int_(0)^(2015)(e^(x))/(1+x^(n))dx , then find the value of lim_(nto oo)f(n)

if f(x) = x^n then the value of f(1) - (f'(1))/(1!) + (f''(1))/(2!) + ---+((-1)^n f''^--n times (1))/(n!)

If f(x) is a polynomial of degree n such that f(0)=0 , f(x)=1/2,....,f(n)=n/(n+1) , ,then the value of f (n+ 1) is

If f(x)=(a^x)/(a^x+sqrt(a ,)),(a >0), then find the value of sum_(r=1)^(2n1)2f(r/(2n))

If f(x)=x^(n),"n" epsilon N , then the value of f(1)-(f^(')(1))/(1!)+(f^(")(1))/(2!)-(f^''')(1)/(3!)+…+(-1)^(n)(f^(n)(1))/(n!) is

If the sum of the series 1+(3)/(2)+(5)/(4)+(7)/(8)+……+((2n-1))/((2)^(n-1)) is f(n) , then the value of f(8) is

If f(x)=(1-x)^n, then the value of f(0)+f^(prime)(0)+(f^('')(0))/(2!)+(f^(''')(0))/(3!)+......(f^n(0))/(n !)dot

Let f(x)=lim_(n rarr oo)(x^(2n-1)+ax^(2)+bx)/(x^(2n)+1). If f(x) is continuous for all x in R then find the values of a and b.

Let f: N to N be defined as f(n) = (n+1)/(2) when n is odd and f(n) = (n)/(2) when n is even for all n in N . State whether the function f is bijective. Justify your answer.