Proof of the power series 1 + $x^2$ + $x^3$ + $\ldots$ + $x^n$ = $\frac{1}{1-x}$
2678
Values of $\sum_{n=0}^\infty x^n$ and $\sum_{n=0}^N x^n$
63829
Use Cauchy product to find a power series represenitation of $1 \over {(1-x)^3}$
27304
Proving $ 1+\frac{1}{4}+\frac{1}{9}+\cdots+\frac{1}{n^2}\leq 2-\frac{1}{n}$ for all $n\geq 2$ by induction
154544
Prove that $ \sum_{n=0}^\infty \frac{z^{2^n}}{1-z^{2^{n+1}}}=\frac{z}{1-z} $
128309
Use Mathematical Induction to prove that $\frac{1}{1 \cdot 2} + \frac{1}{2 \cdot 3} +...+\frac{1}{n(n+1)}=1-\frac{1}{n+1}$
13902
Show that $\frac{1}{x_1^2}+\frac{1}{4\cdot x_2^2}+\ldots+\frac{1}{n^2\cdot x_n^2}\leq\frac{3n-2}{2n-1}$.
15205
Proving that the series 1 + ... + $1 / \sqrt{x}$ < $2 \sqrt{x}$
112907
Math Induction Proof: $(1+\frac1n)^n < n$
87411
Prove that $\sqrt{x_1}+\sqrt{x_2}+\cdots+\sqrt{x_n} \geq (n-1) \left (\frac{1}{\sqrt{x_1}}+\frac{1}{\sqrt{x_2}}+\cdots+\frac{1}{\sqrt{x_n}} \right )$
146546
Proving for all integer $n \ge 2$, $\sqrt n < \frac{1}{\sqrt 1} + \frac{1}{\sqrt 2}+\frac{1}{\sqrt 3}+\cdots+\frac{1}{\sqrt n}$
85626
prove $\sum_{i=1}^{n}(x_i-\bar{x})^2\lt\sum_{i=1}^{n}(x_i-a)^2$
80432
Is the series convergent $x + x^{1+\frac{1}{2}}+x^{1+\frac{1}{2}+ \frac{1}{3}}+\cdots$
150642
How to prove $\sum^n_{i=1} \frac{1}{i(i+1)} = \frac{n}{n+1}$?
14064
Proof by induction that $\sum_{i=1}^n \frac{i}{(i+1)!}=1- \frac{1}{(n+1)!}$
15838
Induction Proof that $x^n-y^n=(x-y)(x^{n-1}+x^{n-2}y+\ldots+xy^{n-2}+y^{n-1})$
60673
To prove $\sum_{cyc}\frac{1}{a^3+b^3+abc} \le \frac{1}{abc}$
30688
Prove that $\frac{x_1}{1+x_2+x_3+\ldots+x_n}+\frac{x_2}{1+x_1+x_3+\ldots+x_n}+\ldots+\frac{x_n}{1+x_1+x_2+\ldots+x_{n-1}}\ge\frac{n}{2n-1}$.