Ok, so I have the problem lim n-> infinity (1 +5/n)^(4n)(adsbygoogle = window.adsbygoogle || []).push({});

So looking at it without trying anything I can see for n arbitrarily large 5/n goes to 0. That means (1+0)^(infinity). One to the power of any real number is one. However by looking at the definition of e as x->infinity I can say (1+ 1/x)^x=e^1

So (1+5/x)^(4x)= e^5*4 or e^20, which is not quite one. Where am I going wrong here?

Also I have the problem lim n-> infinity (n/n+3)^2n . I can same the same thing here as n tends to go to infinity I would have infinity over infinity which is 1? so one raised to infinity is one. I know I am incorrect in this assumption but why?

How would I go on solving this problem?

LIM N-> infinity

(N/N+3)^(2N) =

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# Limit and Series

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