Pattern for $x^n + \frac{1}{x^n}$ if $x + \frac{1}{x} = \frac{1+\sqrt 5}{2}$
113334
If $x+\frac{1}{x}=\frac{1+\sqrt{5}}{2}$ then $x^{2000}+\frac{1}{x^{2000}}= $?
153594
When is $1^5 + 2^5 + \ldots + n^5$ a square?
84147
Evaluating $\sum_{n=1}^\infty \frac{2^{2n-1}}{5^{n+1}}$
72410
If $\alpha_1,\alpha_2,\ldots,\alpha_n$ be the roots of the equation $x^n+1$
134176
For $x$ and $\lambda$ complex, if $|x| \gt \frac{1}{2} + \sqrt{\frac{5}{4} + |\lambda|}$ then $|x^2+\lambda| \gt |x| +1$
57491
Double induction example: $ 1 + q + q^2 + q^3 + \cdots + q^{n-1} + q^n = \frac {q^{n+1}-1}{q-1} $
145444
Solve $\dfrac{1}{1+\frac{1}{1+\ddots}}$
156356
Proof that $x^n+\frac{1}{x^n}\in \mathbb Z$ by complete induction
113016
Remainder form of Taylor polynomial at $x_0$: $ \frac{1}{n!}f^{(n)}(x_0 +\theta(x-x_0))(x-x_0)^n$ with $\theta \to \frac{1}{n+1}$ as $ x \to x_0$
124248
$1+\frac {1}{4}(1+\frac {1}{4}) +\frac {1}{9}(1+\frac {1}{4} +\frac {1}{9})+....$
13291
Proving $\sum_{k=1}^n\frac1{\sqrt k}<2\sqrt n$ by induction
63474
Showing $\sum_{i = 1}^n\frac1{i(i+1)} = 1-\frac1{n+1}$ without induction?
140342
$\frac {1}{5}-\frac{1.4}{5.10}+\frac{1.4.7}{5.10.15}-\cdot\cdot\cdot\cdot\cdot\cdot\cdot$
132169
$x^{2000} + \frac{1}{x^{2000}}$ in terms of $x + \frac 1x$.
14435
Show by induction: $(1+\frac{1}{n})^{n}<n$
36906
Prove that $x^n+x^{-n} \in \mathbf{N}$ if $x+\frac1x \in \mathbf{N}$
117816
Is $\frac{x^2+x}{x+1}$ a polynomial?