`S=sum_(n=1)^99(5^(100))/((25)^n+5^(100))` Find [S]

Let t_(100)=sum_(r=0)^(100)(1)/(("^(100)C_(r ))^(5)) and S_(100)=sum_(r=0)^(100)(r )/(("^(100)C_(r ))^(5)) , then the value of (100t_(100))/(S_(100)) is (a) 1 (b) 2 (c) 3 (d) 4

Let t_(100)=sum_(r=0)^(100)(1)/(("^(100)C_(r ))^(5)) and S_(100)=sum_(r=0)^(100)(r )/(("^(100)C_(r ))^(5)) , then the value of (100t_(100))/(S_(100)) is (a) 1 (b) 2 (c) 3 (d) 4

If S=sum_(n=1)^(10)(2n+(1)/(2)), then S

Find the value of S_(n)=sum_(n=1)^(oo)(3^(n)*5^(n))/((5^(n)-3^(n))(5^(n-1)-3^(n+1))) and hence s_(oo)

S_(n)=sum_(n=1)^(n)(n)/(1+n^(2)+n^(4)) then S_(10)S_(20)

Let f be a real valued function defined on R (the set of all real numbers) such that f(1)=f(-1)=5 and whose graph of f is symmetrical with respect to the lines x=+-1. Given sum_(r=50)^(99)f((r)/(100)) and sum_(r=50)^(150)f((-r)/(100))=5. If S=sum_(r=50)^(150)f((r)/(100))+sum_(r=50)^(150)f((-r)/(100)). Then find S .

Evaluate S=sum_(n=0)^(n)(2^(n))/((a^(2^(n))+1))( where a>1)

sum_(n=6)^(100)(*^(n+1)C_(4))/(^nC_(5)*n-1)C_(5) is equal to

sum_(n=6)^(100)(*^(n+1)C_(4))/(^nC_(5)*n-1)C_(5) is equal to