$x_1=\sin(x_0)>0, x_{n+1}=\sin(x_n)$, prove $\sqrt{\frac{n}{3}}x_n \to 1$ as $n \to \infty$
16970
Convergence of $\sqrt{n}x_{n}$ where $x_{n+1} = \sin(x_{n})$
61696
Prove that $\{x_1=1,\,x_{n+1}=\frac {x_n}2+\frac 1{x_n} \}$ converges when $n \to \infty$
119147
How to prove that $\sum_{n=1}^{\infty}\frac{|\sin{(n\theta_0)}|}{n}$ diverges for given $\theta_0\in (0,\pi)$?
82968
Find $(a,b)$ such that $\lim\limits_{x\to 0}\frac{f(x)}{x}=1$ implies $\lim\limits_{x\to 0}\frac{x(1+a\cos x)-b\sin x}{(f(x))^3}=1$
70746
Proving that $(x_n)_{n=1}^{\infty}$ is a Cauchy sequence.
122820
Prove $\lim_{n\to\infty}x_n=2$ Given $\lim_{n \to \infty} x_n^{x_n} = 4$
95085
Prove by induction $ \sin x + \sin 2x + ... + \sin nx = \frac {\sin (\frac {n + 1} {2} x)} {\sin \frac{x}{2}} \sin \frac{nx}{2} $
89728
Prove that $1<\frac{1}{n+1}+\frac{1}{n+2}+...+\frac{1}{3n+1}$
89265
Proving that $x - \frac{x^3}{3!} 0$
42251
Limit of non-negative real root of $x^n+x^{n-1}+x-1=0$ as $n \to \infty$
156610
To prove the limit of $\frac{x^2+2\cos x-2}{x\sin^3 x}$ at zero is $1/12$
123476
Prove $[\sin x]' = \cos x$ without using $\lim\limits_{x\to 0}\frac{\sin x}{x} = 1$
16253
Proof that $|\sin(nx)| \le n|\sin(x)|$
143227
Show that: $\lim \limits_{n\to\infty}\frac{x_n-x_{n-1}}{n}=0 $
156766
Prove that $\sqrt{\frac{n}{n+1}}\notin \mathbb{Q}$
66441
Prove that $|x|<1$ implies that $\lim_{n \to \infty} x^n=0$
133190
Calculus - Prove $\lim_{n \to \infty} \frac{x^n}{n!}=0$