Let `a_n=sum_(k=1)^n1/(k(n+1-k)),` then for `n >= 2`

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

Let S_(n)=sum_(k=1)^(4n)(-1)(k(k+1))/(2)k^(2). Then S_(n) can take value (s)1056b.1088c.1120d.1332

Let a_(n)=sum_(k=1)^(n)tan^(-1)((1)/(k^(2)+k+1));n>=1 ,then lim_(n rarr oo)n^(2)(e^(a_(n)+1)-e^(a_(n)))=

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

Let S_(n)=sum_(k=1)^(n) (n)/(n^(2)+nk+k^(2)) and T_(n)=sum_(k=0)^(n-1)(n)/(n^(2)+nk+k^(2)) for n= 1,2,3..., then

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

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

If for n in N,sum_(k=0)^(2n)(-1)^(k)(2nC_(k))^(2)=A, then find the value of sum_(k=0)^(2n)(-1)^(k)(k-2n)(2nC_(k))^(2)