L_(n rarr oo)(1.1!+2.2!+.........+n*n!)/((n+1)!)=

lim_ (n rarr oo) (1 * 1! + 2 * 2! + ...... n * n!) / ((n + 1)!)

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

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

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

Let a = lim_(n rarr oo) (1+2+3+.....+n)/(n^(2))= , b = lim_(n rarr oo) (1^(2)+2^(2)+.....+n^(2))/(n^(3))= then

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

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

Evaluate the following limit: (lim)_(n rarr oo)((n+2)!+(n+1)!)/((n+2)!-(n+1)!)

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

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