`lim_(n rarr oo)sum_(k=1)^(n)((1)/(k!)-(1)/((k+3)!)))`

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

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))

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

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

alpha=lim_(n rarr oo)sum_(i=1)^(n)sum_(j=1)^(i)(j)/(n^(3)), then [(1)/(alpha)-1] is

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

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

If lim_(n rarr oo)sum_(k=1)^(n)(k^(2)+k)/(n^(3)+k) can be expressed as rational (p)/(q) in the lowest form then the value of (p+q), is

lim_(nrarroo) sum_(k=1)^(n)(k^(1//a{n^(a-(1)/(a))+k^(a-(1)/(a))}))/(n^(a+1)) is equal to