Let `f(n) =( sum_(r=1)^ n (1/r))/(sum_(k=1)^n k/(2n-2k+1)(2n-k+1))` then `f(100)=`

sum_(k =1)^(n) k(1 + 1/n)^(k -1) =

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

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

Let a_(n)=sum_(k=1)^(n)(1)/(k(n+1-k)), then for n>=2

Let f(1)=1 and f(n)=2 sum_(r=1)^(n-1)f(r) then sum_(n=1)^(m)f(n)=

For n in N, let a_(n)=sum_(k=1)^(n)2k and b_(n)=sum_(k=1)^(n)(2k-1)* then lim_(n rarr oo)(sqrt(a)_(n)-sqrt(b_(n))) is equal to

Let U_(n)=sum_(k=1)^(n)(n)/(n^(2)+k^(2)),S_(n)=sum_(k=0)^(n-1)(n)/(n^(2)+k^(2)) then

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