00:01
In this question we need to determine whether the sequence n -cube e to the power minus n converges and if it converges then we need to find its limit.
00:13
Let's see how to solve this question.
00:16
Consider a -n is equal to n -cube -e -to -the -power minus -n.
00:28
Now to find the limit of the sequence, apply the l -hospital rule.
00:44
So, we can write limit n tends to infinity an is equal to limit n tends to infinity n cubed a to the power minus n.
01:04
So this will be equal to limit n tends to infinity n cube upon a to the power n.
01:18
Now differentiate the numerator and denominator separately.
01:23
So this will be equal to limit n tends to infinity 3 n squared upon e to the power n.
01:35
And this will be equal to 3 into limit n tends to infinity n square upon e to the power n.
01:46
Now again apply the l hospital rule.
01:57
Again apply l hospital rule...