query: How do I calculate/prove limits for exponential functions: $\lim\limits_{n \rightarrow \infty}{\frac {2^{n+1}+3^{n+1}}{2^n + 3^n}} = 3$
positive_passages.docid: 28666
positive_passages.text: simple convergence test $\lim_{n \to \infty} \frac{2^{n+1}+3^{n+1}}{2^n+3^n}$
negative_passages.docid: 122990
negative_passages.text: How can I prove that $\lim\limits_{n\to\infty}\frac{n+\sin n}{n+1} = 1$
negative_passages.docid: 19100
negative_passages.text: Find $\lim \limits_{n \to \infty}{1*4*7*\dots(3n+1) \over 2*5*8* \dots (3n+2)}$
negative_passages.docid: 41366
negative_passages.text: Compute $\lim\limits_{n\to\infty} \left(1+\frac{1}{n}\right)\left(1+\frac{2}{n}\right)^{{1}/{2}}\cdots\left(1+\frac{n}{n}\right)^{{1}/{n}}$
negative_passages.docid: 144310
negative_passages.text: How would you prove that $\lim\limits_{n\to\infty}(\sqrt{4n^2+n}-2n)=\frac14$?
negative_passages.docid: 30181
negative_passages.text: Proving that $\lim\limits_{x \to 0}\frac{e^x-1}{x} = 1$
negative_passages.docid: 99752
negative_passages.text: how does one solve $\lim_{n\to \infty} (\frac{n^{2}-2n+1}{n^{2}-4n+2})^{n}$
negative_passages.docid: 152557
negative_passages.text: Calculate $ \lim\limits_{n \to \infty} \sum\limits_{k=0}^n \frac{2^{k-1}}{a^{2k-1}+1} $
negative_passages.docid: 102414
negative_passages.text: $\lim_{n \to \infty} (\frac{(n+1)(n+2)\dots(3n)}{n^{2n}})^{\frac{1}{n}}$ is equal to :
negative_passages.docid: 36384
negative_passages.text: Q: $\lim_{n\to \infty}\left(1 + \frac{1}{n}\right)^{n} = e$
negative_passages.docid: 111418
negative_passages.text: Finding lim${_{n \rightarrow \infty}}\left( \frac{n^3}{2^n} \right)$
negative_passages.docid: 61300
negative_passages.text: Evaluating $\lim\limits_{n\to\infty} \left(\frac{1^p+2^p+3^p + \cdots + n^p}{n^p} - \frac{n}{p+1}\right)$
negative_passages.docid: 156557
negative_passages.text: How to compute $\lim_{n\rightarrow\infty}e^{-n}\left(1+n+\frac{n^2}{2!}\cdots+\frac{n^n}{n!}\right)$
negative_passages.docid: 15292
negative_passages.text: Elementary proof for $\lim\limits_{n \to\infty}\frac{n!e^n}{n^n} = +\infty$
negative_passages.docid: 98367
negative_passages.text: Limit of $\left(\frac{n^2+2}{2n^2+1}\right)^{n^2}$
negative_passages.docid: 61487
negative_passages.text: Limit of $\frac1n\sqrt[n]{(n+1)(n+2)(n+3)...(n+n)}$
negative_passages.docid: 123248
negative_passages.text: How can I show $\lim_{n\to\infty}\prod_{j}^n\frac{\sin(jn^{-3/2}u)}{jn^{-3/2}u}=e^{-u^2/18}$?