I am trying to solve this sequence limit: limn→+∞n2(e−(1+1n)n) but the only elementary way I found to solve it is to prove that $$ \left(1+\frac1n\right)^n+\frac1n.
However proving the first inequality is not straightforward so I would like to know if there exist a more direct way to solve it.
Answer
I used the fact : limn→∞n(e−(1+1n)n)=e2
For the large n,
n2(e−(1+1n)n)∼e2n⟶∞wheren⟶∞
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