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Just to clarify that is 917^(n+100) on the top

Just going to throw a joke out here because it's 4:04am... "The limit does not exist!" - Mean Girls

That's not really the answer though :P

oops
\[0\times 917^{100}=0\]

wait, left something out.

ahhh, just imagine the bottom line as n(955)

But this part
\[\frac{917^{n+100}}{n}\ne 0\]
It's of the form
\[\frac{\infty}{\infty}\]