Definition of $ 1 + \frac{1}{2+\frac{1}{3+\frac{1}{4+\frac{1}{\ddots}}}}$
53672
Convergence of a Harmonic Continued Fraction
120430
A question about how to express a fraction as ${1\over q_1}+{1\over q_2}+ \cdots+{1\over q_N}$
73191
Proving that $\frac{1}{1\cdot 2} + \frac{1}{2\cdot 3} + \frac{1}{3 \cdot 4} +\ldots + \frac{1}{n(n+1)} = \frac{n}{n+1}$
4816
How to solve $\frac 1{1.2.3}+\frac 1{2.3.4}+\frac 1{3.4.5}+...$
106028
Sum of $\frac{1}{(2n)(2n+1)}$ from $1$ to infinity
4340
Why does $1+2+3+\cdots = -\frac{1}{12}$?
112658
Difference between $\sum_{i=1}^{k}{\frac{s_i}{kn_i}}$ and $\frac{\sum_{i=1}^{k}{s_i}}{\sum_{i=1}^{k}{n_i}}$
23576
Calculating $1+\frac13+\frac{1\cdot3}{3\cdot6}+\frac{1\cdot3\cdot5}{3\cdot6\cdot9}+\frac{1\cdot3\cdot5\cdot7}{3\cdot6\cdot9\cdot12}+\dots? $
8905
Sum the series $\frac{3}{1⋅2⋅4}+\frac{4}{2⋅3⋅5}+ \frac{5}{3⋅4⋅6}+...\text{(upto n terms)}$
46401
Value of $\frac{\sqrt{10+\sqrt{1}}+\sqrt{10+\sqrt{2}}+\cdots+\sqrt{10+\sqrt{99}} }{\sqrt{10-\sqrt{1}}+\sqrt{10-\sqrt{2}}+\cdots+\sqrt{10-\sqrt{99}}}$
55061
Evaluating the sum after reordering an infinite series $1-\frac {1} {2}+\frac {1} {3}-\frac {1} {4}+\ldots $
141357
Is $1+2+3+4+\cdots=-\frac{1}{12}$ the unique ''value'' of this series?
34362
Are there any examples of $\frac{a}{b}+\frac{c}{d}=\frac{a+c}{b+d}$?
58262
Find the sum of the series $1+\frac{1}{3}\cdot\frac{1}{4}+\frac{1}{5}\cdot\frac{1}{4^2}+\frac{1}{7}\cdot\frac{1}{4^3}+\cdots$
37059
limit of the sum $\frac{1}{n+1}+\frac{1}{n+2}+\cdots+\frac{1}{2n} $
47783
why $1+\frac{1}{1+\frac{1}{\frac{1}{1+\dots}}}$ cannot be equal to $\frac{1-\sqrt{5}}{2}$
42271
Infinite Series $1+\frac12-\frac23+\frac14+\frac15-\frac26+\cdots$