I know the fact that $\lim_{n \to \infty} (1+1/n)^n$ tends to $e$, but how do I use this fact to find the limit of $(1-\frac{1}{2n}-\frac{1}{2n^2})^n$ as $n$ tends to infinity?
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Welcome to Maths SE. Please use MathJax. – Toby Mak Apr 25 '21 at 12:30
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1Does this answer your question? How to show $\lim_{k\rightarrow \infty} \left(1 + \frac{z}{k}\right)^k=e^z$ The $\frac{1}{2n^2}$ term is negligble (take out a common factor). – Toby Mak Apr 25 '21 at 12:32
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$(1-\frac{1}{2n}-\frac{1}{2n^2})^n=e^{n\ln(1-\frac{1}{2n}-\frac{1}{2n^2})}$ – Svyatoslav Apr 25 '21 at 12:33
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$\ln(1+\epsilon)=\epsilon-\frac{1}{2}\epsilon^2+\frac{1}{3}\epsilon^3-...$ – Svyatoslav Apr 25 '21 at 12:38