Find the limit of sequence

Question

Find the limit of sequence : a_n= 2n²+5n+7 / 4n²+5n+6

Answer 1

Divide the numerator and denominator by n² to get lim_n→∞ [(2 + 5/n + 7/n²) / (4 + 5/n + 6/n²)] =

(2+0+0) / (4+0+0) = 2/4 = 1/2

Answer 2

lim n→∞ a_n= lim n→∞ (2n²+5n+7)/(4n²+5n+6) = 2/4 = 1/2