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

Let S_(n)=sum_(r=1)^(oo)(1)/(n^(r)) and sum_(n=1)^(k)(n-1)S_(n)=5050, then k=

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 S_(n)=sum_(r=0)^(n)(1)/(nC_(r)) and sum_(r=0)^(n)(r)/(nC_(r)), then (t_(n))/(S_(n))=

Given S_(n)=sum_(r=0)^(n)(1)/(2^(r)),S=sum_(r=0)^(oo)(1)/(2^(r)). If S-S_(n)<(1)/(1000), then least value of ln'(A)8 (B) 9(C)10(D)11

If sum_(r=1)^n r=55 ,\ fin d\ sum_(r=1)^n r^3dot

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 is equal to

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 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