I need to find the limit:
limn→∞((1+1n2)n2e)n
So I know that the limit is 1.
Using Squeeze theorem
?≤((1+1n2)n2e)n≤(ee)n→ 1
What should be instead ? ? Is it possible to solve in another way?
Unfortunately, I can't use L'Hôpital Rule or Series Expansion in this task.
Answer
Note that:
((1+1n2)n2(1+1n2)n2+1)n=(1+1n2)−n≤((1+1n2)n2e)n≤(ee)n=1
Since:
(1+1n2)−n→1
By Squeeze Theorem:
limn→∞((1+1n2)n2e)n=1
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