when the sum of some fractions equal to 1.
49851
when the sum of some fractions be $1$
55777
A tricky sum to infinity
79950
Prove that for an integer n larger than or equal to 2, the period for the decimal expression of the rational number $\frac{1}{n}$ is at most n -1.
63474
Showing $\sum_{i = 1}^n\frac1{i(i+1)} = 1-\frac1{n+1}$ without induction?
109365
Prove that 1/2 + 1/4 + 1/8 ....... = 1
126161
Interesting property of finite integer sequence with sum 1
93756
$1+\frac{1}{2} +\frac{1}{3} +...+\frac{1}{p-1} =\frac{a}{b}$
41792
If $abc=1$, then $\frac{a^{n+2}}{a^n+(n-1)b^n}+\frac{b^{n+2}}{b^n+(n-1)c^n}+\frac{c^{n+2}}{c^n+(n-1)a^n} \geq \frac{3}{n} $
37007
Evaluating $\sum_{k=1}^{n} \frac{1}{k(k+1)}$
89367
Calculate $ S =\sum_{k=1}^n\frac {1}{k(k+1)(k+2)}. $
105164
If $abc=1$, prove that $\frac{2}{(a+1)^2+b^2+1} + \frac{2}{(b+1)^2+c^2+1} + \frac{2}{(c+1)^2+a^2+1} \le 1$.
50606
Find $\sum\limits_{k\, \text{ odd}} \frac{2(k^2-1)}{k^4+k^2+1}$
129236
Continued fraction for $\frac{1}{e-2}$
8666
Let us define a series $\{a(n)\}$ such that $a(n)= a(n-1) + \frac{1}{a(n-1)}$
95786
Sum $\frac{1}{6} + \frac{5}{6\cdot 12} + \frac{5\cdot 8}{6\cdot 12\cdot 18} + \frac{5\cdot 8\cdot 11}{6\cdot 12\cdot 18\cdot 24}+\ldots$
41645
Checking my understanding: $1 - 1 + 1 - 1 + 1 - ... = \frac{1}{2}$
121554
Finding $\sum\frac{1}{2^n(n+1)}$