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**spruancejr** Given lim $\displaystyle S_n=(1+\dfrac{1}{n})^n \rightarrow e$

Find

1)lim $\displaystyle S_n=(1+\dfrac{1}{2n})^{2n} \rightarrow ?$

2)lim $\displaystyle S_n=(1+\dfrac{1}{n})^{2n} \rightarrow ?$

Attempt:

I see that $\displaystyle \dfrac{1}{2n}$ converges to zero which makes it no different than $\displaystyle \dfrac{1}{n}$ so we're left with $\displaystyle S_n=(1+\dfrac{1}{n})^{2n} \rightarrow ?$ which should make both problems #1 and #2 have a limit of $\displaystyle e^2$.

However, the back of the book indicates that #1 has a limit of e and #2 has a limit of $\displaystyle e^2$