Showing that $f_n$ is the number closest to $\frac{1}{\sqrt{5}}(\frac{1+\sqrt{5}}{2})^n$
100781
Prove the $n$th Fibonacci number is the integer closest to $\frac{1}{\sqrt{5}}\left( \frac{1 + \sqrt{5}}{2} \right)^n$
72600
Proof that $n!\leq {(\frac{n+1}{2})}^{n}$
108429
Show that if $x_n \to x$ then $\sqrt{x_n} \to \sqrt{x}$
151171
Distance of nearest zero of an analytic function
1570
Show that log $Fib_{n}$ is $\theta(n)$
131692
How to show that $f_{0}f_{1}+f_{1}f_{2}+...+f_{2n-1}f_{2n} = f^{2}_{2n}$
50930
Proving the continued fraction representation of $\sqrt{2}$
75329
Use induction to prove that $F_n \ge \sqrt 2 ^n$ for $n \ge 6$
149056
Prove that for all $n\geqslant 1$ we have $F_n<{\left(\frac 74\right)}^n$.
116901
Monotonicity of $\frac{n}{\sqrt[n]{(n!)}}$
88425
Prove that $\,\sqrt [n] n < 1 + \sqrt{\frac{2}{n}}\,$
21921
Showing that $|f(z)| \leq \prod \limits_{k=1}^n \left|\frac{z-z_k}{1-\overline{z_k}z} \right|$
153226
Proof of $\sum_{k = 1}^{n} \frac{1}{k^{2}} < 2 - \frac{1}{n}$
14435
Show by induction: $(1+\frac{1}{n})^{n}<n$
49750
Proof of the square root inequality $2\sqrt{n+1}-2\sqrt{n}<\frac{1}{\sqrt{n}}<2\sqrt{n}-2\sqrt{n-1}$
148163
Show that if m/n is a good approximation of $\sqrt{2}$ then $(m+2n)/(m+n)$ is better
12031
Asymptotic behavior of the sequence $a_n=\sqrt{n+a_{n-1}}$