lim_(n rarr oo)sum_(k=0)^(n)(1)/(^nC_(k))

Let S_(k)=lim_(n rarr oo)sum_(i=0)^(n)(1)/((1+k)^(i)). Then sum_(k=1)^(n)kS_(k) equals:

The value of lim_(n rarr oo)sum_(k=1)^(n)log(1+(k)/(n))^((1)/(n)) ,is

Find the value of lim_(n rarr oo)sum_(k=1)^(n)((k)/(n^(2)+k))

The value of int_(0)^(1)lim_(n rarr oo)sum_(k=0)^(n)(x^(k+2)2^(k))/(k!)dx is:

The value of Lim_(n rarr oo)sum_(k=1)^(n)(n-k)/(n^(2))cos((4k)/n) equals

For a natural number n,let a_(n)=int_(0)^((pi)/(4))(tan x)^(2n)dx. Now answer the following questions.Express (1)a_(n+1) in terms of a_(n)(2) Find lim_(n rarr oo)a_(n)(3) Find lim_(n rarr oo)sum_(k=1)^(n)(-1)^(k-1)(a_(k)+a_(k-1))

Evaluate lim_(n rarr oo)sum_(k=1)^(n)quad (k)/(n^(2)+k^(2))

The value of lim_(n rarr oo)sum_(k=1)^(n)(6^(k))/((3^(k)-2^(k))(3^(k+1)-2^(k+1))) is equal to

Find the value of lim_(n rarr oo)sum_(k=1)^(n)(k^(2)+k-1)/((k+1)!) .