Prove that 1/2 + 1/4 + 1/8 ....... = 1
2678
Values of $\sum_{n=0}^\infty x^n$ and $\sum_{n=0}^N x^n$
80004
Why is $1/i$ equal to $-i$?
106868
Prove that $x+\frac1{4x} ≥ 1$ for $x>0$
52113
Proof by Induction $\sum_{i=0}^{k-1} 2^i = 2^k-1$
151154
Prove the inequality $\sqrt\frac{a}{a+8} + \sqrt\frac{b}{b+8} +\sqrt\frac{c}{c+8} \geq 1$ with the constraint $abc=1$
93427
Show that $\sum_{i=1}^{n} \frac {a_i}{1+a-a_i} + \prod_{i=1}^{n} {(1-a_i)} \leq 1$
75387
A proof that $1=2$. May I know why it’s false?
13902
Show that $\frac{1}{x_1^2}+\frac{1}{4\cdot x_2^2}+\ldots+\frac{1}{n^2\cdot x_n^2}\leq\frac{3n-2}{2n-1}$.
31074
Mathematical Induction divisibility $8\mid 3^{2n}-1$
147648
Proving $\frac{a}{a^2-a+1}+\frac{b}{b^2-b+1}+\frac{c}{c^2-c+1}+\frac{d}{d^2-d+1}\le \frac{8}{3}$ given $a+b+c+d=2$
148647
If $\dfrac{4x^2-1}{4x^2-y^2}$ is an integer, then it is $1$
7414
Prove that odd perfect square is congruent to $1$ modulo $8$
79170
$1 + \frac{1}{1+2}+ \frac{1}{1+2+3}+ ... + \frac{1}{1+2+3+...+n} = ?$
13291
Proving $\sum_{k=1}^n\frac1{\sqrt k}<2\sqrt n$ by induction
49851
when the sum of some fractions be $1$
73002
For $n \geq 2$, prove that $(1- \frac{1}{4})(1- \frac{1}{9})(1- \frac{1}{16})...(1- \frac{1}{n^2}) = \frac{n+1}{2n}$
85042
Write $1/1 + 1/2 + ...1/ (p-1)=a/b$ with $(a,b)=1$. Show that $p^2 \mid a$ if $p\geq 5$ is prime [Wolstenholme's theorem]