Lim x—> infinity∞ [(³√n+1)²-(³√n)²] Answer Value ??

1 Answer
Alan N.
Jun 8, 2018

#lim_(n->oo) [(root3 n +1)^2 - (root3 n)^2] ->oo#

Explanation:

#f(n) = [(root3 n +1)^2 - (root3 n)^2]#

#= (n^(2/3) + 2n^(1/3) +1) - n^(2/3)]#

#= 2n^(1/3) +1#

#lim_(n->oo) (2n^(1/3) +1) -> oo#

Hence

#lim_(n->oo) f(n) -> oo#

Related questions
Impact of this question
1956 views around the world
You can reuse this answer
Creative Commons License