Let `S_n=sum_(r=0)^oo 1/n^r and sum_(n=1)^k (n-1)S_n = 5050 then k=` (A) 50 (B) 505 (C) 100 (D) 55

If S_n=sum_(r=0)^n 1/(nC_r) and t_n=sum_(r=0)^n r/(nC_r), then t_n/S_n=

If sum_(r=1)^n r=55 , F i nd sum_(r=1)^n r^3dot

Find the sum_(k=1)^(oo) sum_(n=1)^(oo)k/(2^(n+k)) .

Let S_n=sum_(k=0)^n n/(n^2+kn+k^2) and T_n=sum_(k=0)^(n-1) n/(n^2+kn+k^2) for n=1,2,3... then (a) S_n lt pi/3sqrt(3) b) S_n gt pi/3sqrt(3) (c) T_n lt pi/3sqrt(3) (d) T_n gt pi/3sqrt(3)

If f (n) = sum_(s=1)^n sum_(r=s)^n "^nC_r "^rC_s , then f(3) =

If sum_(r=1)^n t_r= (n(n+1)(n+2))/3 then sum _(r=1)^oo 1/t_r= (A) -1 (B) 1 (C) 0 (D) none of these

Let sum_(r=1)^(n) r^(6)=f(n)," then "sum_(n=1)^(n) (2r-1)^(6) is equal to

sum_(r=1)^(n) r^(2)-sum_(r=1)^(n) sum_(r=1)^(n) is equal to

Prove that sum_(r=0)^ssum_(s=1)^n^n C_s^n C_r=3^n-1.

If sum_(r=1)^n r^4= a_n then sum_(r=1)^n(2r-1)^4)= (A) a_(2n)+a_n (B) a_(2n)-a_n (C) a_(2n)-16a_n (D) a_(2n)+16b_n