Find `lim_(n->oo)(2n-1)(2n)n^2(2n+1)^(-2)(2n+2)^(-2)`

Find lim_(n rarr oo)(2n-1)(2n)n^(2)(2n+1)^(-2)(2n+2)^(-2)

FInd lim_(n rarr oo)(2n-1)2^(n)(2n+1)^(-1)2^(1-n)

lim_(n rarr oo)(e^(2n)(n!)^(2))/(2n^(2n+1))

The value of lim_(n to oo)[(n)/(n^(2))+(n)/(n^(2)+1^(2))+(n)/(n^(2)+2^(2))+...+(n)/(n^(2)+(n-1)^(2))] is :

lim_(n rarr oo){(1)/(2)(n^(2)+1)sin^(-1)((2n)/(1+n^(2)))-n}=

Evaluate the following (i) lim_(n to oo)((1)/(n^(2))+(2)/(n^(2))+(3)/(n^(2))....+(n-1)/(n^(2))) (ii) lim_(n to oo)((1)/(n+1)+(1)/(n+2)+....+(1)/(2n)) (iii) lim_(n to oo)((n)/(n^(2)+1^(2))+(n)/(n^(2)+2^(2))+....+(n)/(2n^(2))) (iv) lim_(n to oo)((1^(p)+2^(p)+.....+n^(p)))/(n^(p+1)),pgt0

lim_(n rarr oo)(3^(n+1)+2^(n+2))/(3^(n-1)+2^(n-2)) =

lim_(n to oo)[(n+1)/(n^(2)+1^(2))+(n+2)/(n^(2)+2^(2))+....+(1)/(n)]

lim_(n rarr oo)((n^(2)-n+1)/(n^(2)-n-1))^(n(n-1)) is

lim_(n->oo) (1)/(n^(6)){(n+1)^(5)+(n+2)^(5)+...+(2n)^(5)}