`lim_[n->oo][5^[n+1]+3^n-2^[2n]]/[5^n+2^n+3^[2n+3]]`

The value of lim_(x rarr oo)(5^(n+1)+3^(n)-2^(2n))/(5^(n)+2^(n)+3^(2n+1))

S1: lim_(n->oo) (2^n + (-2)^n)/2^n does not exist S2: lim_(n->oo) (3^n + (-3)^n)/4^n does not exist

Consider the following statements : I. lim_(n to oo) ( 2^n +(-2)^n)/(2^n) dos not exist II. lim_(n to oo) ( 3^n +(-3)^n)/(2^n) does not exist then

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

Evaluate : lim_(n-> oo) (1^4+2^4+3^4+...+n^4)/n^5 - lim_(n->oo) (1^3+2^3+...+n^3)/n^5

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

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

lim_(n->oo) (1.2+2.3+3.4+....+n(n+1))/n^3

The value of lim_(n -> oo)(1.n+2.(n-1)+3.(n-2)+...+n.1)/(1^2+2^2+...+n^2)