If `sum_(n=1)^5 1/(n(n+1)(n+2)(n+3))=k/3,` then `k` is equal to :-

sum_(n=1)^oo 1/((n+1)(n+2)(n+3).........(n+k))

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

Given S_(n)=sum_(k=1)^(n)(k)/((2n-2k+1)(2n-k+1)) and T_(n)=sum_(k=1)^(n)(1)/(k) then (T_(n))/(S_(n)) is equal to

lim_ (n rarr oo) sum_ (k = 1) ^ (n) (k) / (n ^ (2) + k ^ (2)) is equals to

If sum_(k=1)^(n)4(k-3)=An^(2)+Bn+C,n in N then |A+B-C| equals

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