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How would one use the squeeze theorem to find the limit $$\lim_{n\rightarrow\infty} (\frac{1+n}{2n})^n$$ ?

Unlike functions that incorporate sine or cosine, it's less apparent to me what the bounds should be.

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Take the bounds: $\frac{1}{2}<\frac{1+n}{2n}<\frac{\frac{n}{2}+n}{2n}=\frac{3}{4}$. They show that the limit should be $0$.

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The sequence consists of positive values, so we have $$0\le (\frac{1+n}{2n})^n=(\frac{1}{2})^n\cdot (1+\frac{1}{n})^n\le (\frac{1}{2})^n\cdot e$$

This immediately shows that the limit is $0$.

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When $n>1$, $\frac{1+n}{2n} \le \frac{3}{4}$

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