query: limit of a sum of powers of integers
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: 131708
negative_passages.text: Sum of powers of natural numbers
negative_passages.docid: 64012
negative_passages.text: Limit of a geometric series
negative_passages.docid: 98941
negative_passages.text: Closed formula for the sums $\sum\limits_{1 \le i_1 < i_2 < \dots < i_k \le n} i_1 i_2 \cdots i_k $?
negative_passages.docid: 54801
negative_passages.text: Limit of some specific "almost Riemann" sums
negative_passages.docid: 33495
negative_passages.text: A limit problem about $a_{n+1}=a_n+\frac{n}{a_n}$
negative_passages.docid: 140458
negative_passages.text: Infinite summation involving exponents
negative_passages.docid: 71797
negative_passages.text: Combinatorial argument for $\sum\limits_{k=i}^{n}\binom{n}{k}\binom{k}{i} = \binom{n}{i}2^{n-i}$
negative_passages.docid: 123675
negative_passages.text: Evaluate the following limit of finite sum
negative_passages.docid: 19898
negative_passages.text: Limit $\lim (1+(a^{1/n}-1) / b)^n$
negative_passages.docid: 80440
negative_passages.text: Limit of $(x_n)$ with $0<x_1<1$ and $x_{n + 1} = x_n - x_n^{n + 1}$
negative_passages.docid: 158124
negative_passages.text: Sum of all the positive integers problem
negative_passages.docid: 37771
negative_passages.text: Sum of a power series $n x^n$
negative_passages.docid: 89698
negative_passages.text: Please help with $\sum\limits_{r=1}^{N}\frac{2r+3}{3^r(r+1)}$
negative_passages.docid: 15259
negative_passages.text: Proving $\prod \limits_{k=0}^{n}(1-a_k) \geq1- \sum\limits_{k=0}^{n}a_k$
negative_passages.docid: 145798
negative_passages.text: Generalizing $\sum \limits_{n=1}^{\infty }n^{2}/x^{n}$ to $\sum \limits_{n=1}^{\infty }n^{p}/x^{n}$
negative_passages.docid: 49029
negative_passages.text: Find the limit $\lim_{n\rightarrow\infty}\sum_{k=1}^{n}\frac{1}{k+n}$