Proving that $a_{n} \rightarrow L$ given that $a_{n}+ 2a_{n+1} \rightarrow 3L$ .
112773
With $y_n$ a sequence of real numbers, prove that if $y_n=x_{n-1}+2x_{n}$ converges then $x_n$ also converges
5927
How to prove $a_1^m + a_2^m + \cdots + a_n^m \geq \frac{1}{a_1} + \frac{1}{a_2} + \cdots + \frac{1}{a_n}$
116966
Prove $\limsup_{n \rightarrow \infty} a_n\geq1$ if $\lim_{n \rightarrow \infty} a_na_{n+1}=1$
154085
$\sum a_i \ln(b_i) \leq \sum a_i \ln(a_i)$ with $\sum a_i = \sum b_i = 1$
96332
Prove by induction that $\sqrt[n+1]{n+1}<\sqrt[n]{n}$ for $n\ge 3$
73553
How is $a_n=(1+1/n)^n$ monotonically increasing and bounded by $3$?
33903
Prove that $(1+a_1) \cdot (1+a_2) \cdot \dots \cdot (1+a_n) \geq 2^n$
145397
How to prove that for every $i$, $a_i = i$
135018
Proving that a sequence has $a_n = a_{n+2}$ for $n$ sufficiently large.
137609
Proving $\lim_{n\rightarrow\infty} n(2^{1/n} - 1) = \log 2$
14581
How do we prove $n^n \mid m^m \Rightarrow n \mid m$?
30630
Proving ${n \choose p} \equiv \Bigl[\frac{n}{p}\Bigr] \ (\text{mod} \ p)$
76696
Using induction to prove $2^{n-1}(1 + a_1a_2\ldots a_n) \geq (1+a_1)(1+a_2)\ldots(1+a_n)$ for $a_i \geq 1$
30770
Prove that $C\left(\bigcup_{\alpha\in I} A_\alpha\right)=\bigcap_{\alpha\in I}C\left(A_\alpha\right)$
120954
Prove that: $\sqrt[3]{a_1^3+ a_2^3 +\cdots+a_n^3} \le \sqrt{a_1^2 + a_2^2 +\cdots+a_n^2}$
70926
Showing that for $n\geq 3$ the inequality $(n+1)^n<n^{(n+1)}$ holds
89728
Prove that $1<\frac{1}{n+1}+\frac{1}{n+2}+...+\frac{1}{3n+1}$