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 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

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

sum_ (n = 0) ^ (oo) (1) / (n!) [sum_ (k = 0) ^ (n) (i + 1) int_ (0) ^ (1) 2 ^ (- (k + 1 ) x) dx]

Let f(n)=(sum_(r=1)^(n)((1)/(r)))/(sum_(k=1)^(n)(k)/(2n-2k+1)(2n-k+1))

The value of sum_(r=1)^(n+1)(sum_(k=1)^(n)C(k,r-1))=

lim_ (n rarr oo) n sum_ (k = 0) ^ (n-1) sum_ (k = 0) ^ (n-1) int _ ((k) / (n)) ^ ((k + 1) / ( n)) sqrt ((x- (k) / (n)) ((k + 1) / (n) -x)) dx is (pi) / (k) then k