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)=(a^(x))/(a^(x)+sqrt(a))(agt0),g(n)=sum_(r=1)^(2n-1)2f((r)/(2n)) . Find te value g(4)

Let F(x)= F(x)=int_0^xtf(t)dt] and F(x^2)=x^4+x^5 then find the value of sum_(r=1)^12f(r^2)

If sum_(r=1)^(n)T_(r)=n(2n^(2)+9n+13); then find the value of sum_(r=1)^(n)sqrt(T_(r))

If f(x) is a function such that f(x-1)+f(x+1)=sqrt(3)f(x) and f(5)=10 then the sum of digit of the value of sum_(r=0)^(19)f(15+12r) is

If sum_(r=1)^(n)r^(4)=F(x), then prove that the value of sum_(n=1)^(n)r(n-r)^(3) is (1)/(4)[n^(3)(n+1)^(2)-4F(x)]

If a=(e^(2 pi i))/(7) and f(x)=A_(0)+sum_(k=1)^(20)A_(k)x^(k) then the value of sum_(r=0)^(6)f(a^(r)x)=n(A_(0)+A_(n)x^(n)+A_(2n)x^(2n)), then the value of n is

If f(x+y+z)=f(x)+f(y)+f(z) with f(1)=1 and f(2)=2 and x,y, z epsilonR the value of lim_(xtooo)sum_(r=1)^(n)((4r)f(3r))/(n^(3)) is ……….

If C_(r) be the coefficients of x^(r) in (1 + x)^(n) , then the value of sum_(r=0)^(n) (r + 1)^(2) C_(r) , is