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1. The problem statement, all variables and given/known data

I'm trying to calculate the limit of the following sequence:

an:= ([itex]\frac{n^{2}+10}{n^{2}-5n}[/itex])[itex]^{(3n^{2}+2)}[/itex]

2. The attempt at a solution

Ok so I got this so far:

an = [itex]\left(\frac{\left(n^2\left(1+\frac{10}{n^2}\right)\right)}{\left(n^2\left(1-\frac{5}{n}\right)\right)}\right)^{n^{2}(3+\frac{2}{n})}[/itex]

[itex]\lim_{n\to \infty }[/itex] an = [itex]\lim_{n\to \infty }[/itex] 1[itex]^{∞}[/itex]

So this is what I got till now and I don't know really how to proceed or how can I approach this problem differently to find the correct solution which is ∞.

Any help, tips are welcome.

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# Calculating a limit of a sequence

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