query: Limit of a Riemann sum $\lim_{n\to \infty} \frac{1^p+2^p+\ldots+n^p}{n^{p+1}}$
positive_passages.docid: 44551
positive_passages.text: What is the result of $ \lim_{n \to \infty} \frac{ \sum^n_{i=1} i^k}{n^{k+1}},\ k \in \mathbb{R} $ and why?
negative_passages.docid: 49029
negative_passages.text: Find the limit $\lim_{n\rightarrow\infty}\sum_{k=1}^{n}\frac{1}{k+n}$
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: 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: 1098
negative_passages.text: Does $\sum\limits_{n=1}^\infty\frac{1}{\sqrt{n}+\sqrt{n+1}}$ converge?
negative_passages.docid: 50334
negative_passages.text: What is $\lim_{n \rightarrow \infty}\sum\limits_{k = 1}^n\frac{k}{n^2}$?
negative_passages.docid: 137155
negative_passages.text: Sum $ \sum\limits_{k=1}^{\infty} \frac{k^2}{2^k}$
negative_passages.docid: 67500
negative_passages.text: Sum of $\lim_{n\rightarrow \infty}\left(\frac{n}{n^2+1}+\frac{n}{n^2+2}+\cdots \cdots \cdots +\frac{n}{n^2+n}\right)$
negative_passages.docid: 28461
negative_passages.text: Show that $\lim_{n\to\infty} \sum_{k=1}^{n} \frac{n}{n^2+k^2}=\frac{\pi}{4}$
negative_passages.docid: 42519
negative_passages.text: $\lim_{n \rightarrow \infty} \sum^n_{k=1} \frac{1}{k+n}$
negative_passages.docid: 25193
negative_passages.text: Find $ \lim _{n\to \infty} \frac{n^1+\dots+n^n}{1^n+\dots+n^n}$
negative_passages.docid: 15822
negative_passages.text: Value of $\lim_{n\to \infty}\frac{1^n+2^n+\cdots+(n-1)^n}{n^n}$
negative_passages.docid: 81654
negative_passages.text: Evaluate $\lim_{n\to\infty} [{1\over kn}+{1\over k(n+1)}+{1\over k(n+2)}+\cdots+{1\over k(n+p-k)}]$ where $k<p$
negative_passages.docid: 103833
negative_passages.text: limit $\lim_{n\to \infty }\sum_{k=1}^{n}\frac{k}{k^2+n^2}$
negative_passages.docid: 41911
negative_passages.text: Use Riemann integral to evaluate the limit $\lim_{n \rightarrow \infty} \frac{\sum_{k=1}^n \sqrt{k}}{\sum_{k=1}^n \sqrt{n+k}}$
negative_passages.docid: 21791
negative_passages.text: Show that $\sum\limits_{k=1}^\infty \frac{1}{k(k+1)(k+2)\cdots (k+p)}=\frac{1}{p!p} $ for every positive integer $p$
negative_passages.docid: 155382
negative_passages.text: Find $ \lim\limits_{{n \to \infty}} \frac1{2^n} \sum\limits_{k=1}^n \frac1{\sqrt{k}} \binom nk$