Is the sequence divergent or convergent?

Question

$lim n→∞ [(6n^3 + sin(11n)^2)/(n^2 +10)]$

989 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-18T20:09:39

See below.

$(6n^3)/(n^2 +10) le (6n^3 + sin(11n)^2)/(n^2 +10)$

and

$(6n^3)/(n^2 +10) = (6n)/(1+10/n)$

and

$lim_(n->oo)(6n)/(1+10/n) = oo$

hence

$lim_( n→∞) [(6n^3 + sin(11n)^2)/(n^2 +10)]$ diverges