query: Closed form for $1+\frac{1}{2} + \frac{1}{3} + \dots + \frac{1}{n}$?
positive_passages.docid: 10357
positive_passages.text: Do harmonic numbers have a “closed-form” expression?
negative_passages.docid: 145444
negative_passages.text: Solve $\dfrac{1}{1+\frac{1}{1+\ddots}}$
negative_passages.docid: 89728
negative_passages.text: Prove that $1<\frac{1}{n+1}+\frac{1}{n+2}+...+\frac{1}{3n+1}$
negative_passages.docid: 87479
negative_passages.text: Closed form for $\sum_{k=0}^{n-p}\binom{n}{k}\binom{n}{p+k}$
negative_passages.docid: 52982
negative_passages.text: Efficient/faster methods to find the general closed form of $\int _0^1\frac{\ln \left(ax^2+b\right)}{x+1}\:dx$
negative_passages.docid: 36457
negative_passages.text: Closed form for $\int \frac{1}{\sin^nx +\cos^mx}dx$
negative_passages.docid: 73191
negative_passages.text: Proving that $\frac{1}{1\cdot 2} + \frac{1}{2\cdot 3} + \frac{1}{3 \cdot 4} +\ldots + \frac{1}{n(n+1)} = \frac{n}{n+1}$
negative_passages.docid: 63553
negative_passages.text: Show that $\frac{1}{(n+1)!}(1+\frac{1}{(n+1)}+\frac{1}{(n+1)^2}+\frac{1}{(n+1)^3}+\cdots)=\frac{1}{n!n}$
negative_passages.docid: 125887
negative_passages.text: Evaluate an infinite product in a closed form $\prod\limits_{n=1}^{\infty} \frac{1}{1+\pi^{1/{2^n}}}$
negative_passages.docid: 68725
negative_passages.text: Find expression for : $ S_n =\sum_{i=1}^{n} \frac{i}{i^4+i^2+1} $
negative_passages.docid: 128415
negative_passages.text: Prove that $1<\frac{1}{1001}+\frac{1}{1002}+\frac{1}{1003}+\dots+\frac{1}{3001}<\frac43$
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: 133160
negative_passages.text: Closed form for $\int_0^\infty\frac{1}{(1+x^2)^s}\,dx$ when $s\in (0.5,\infty)\setminus\mathbb{N}$
negative_passages.docid: 84433
negative_passages.text: Expression generating $\left( \frac{3}{10}, \, \frac{3}{10} + \frac{33}{100}, \, \frac{3}{10} + \frac{33}{100} + \frac{333}{1000}, \dots \right)$
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: 84335
negative_passages.text: Solving for $\sum_{n = 1}^{\infty} \frac{n^3}{8^n}$?
negative_passages.docid: 112036
negative_passages.text: sum of series $\frac{n}{1\cdot 2 \cdot 3}+\frac{n-1}{2\cdot 3\cdot 4}+\frac{n-2}{3\cdot 4 \cdot 5}+\cdots \cdots n$ terms