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**wopashui** $\displaystyle \sqrt{n+1}/2\sqrt{n}$

$\displaystyle \color{red}=\frac{1}{2}\sqrt{\frac{n+1}{n}}=\frac{ 1}{2}\sqrt{1+\frac{1}{n}}$

$\displaystyle (1+1/n)^{2n}$

$\displaystyle \color{red} \left(1+\frac{a}{n^k}\right)^{bn^k} \rightarrow e^{ab}$ as $\displaystyle \color{red} n \rightarrow \infty$

$\displaystyle 2^n/n^2$

Use sandwich theorem ..

$\displaystyle sin n / \sqrt{n}$

Use sandwich theorem ..

$\displaystyle \sqrt {n^2+n} - n$

can anyone tell me the general methods for simplfing these sequence so it looks more obvious?