$a_n=\min\limits_{x+y=1}(x^n+y^n)=\frac{1}{2^{n-1}}$
32149
Proof of the inequality $(x+y)^n\leq 2^{n-1}(x^n+y^n)$
3885
Maximum and minimum of of $f(x)=|x-1|+|x-2|+|x-3|$
15259
Proving $\prod \limits_{k=0}^{n}(1-a_k) \geq1- \sum\limits_{k=0}^{n}a_k$
65827
When $\min_{x \in X,y \in Y} f(x,y) = \min_{x \in X} \min_{y \in Y} f(x,y)$?
119469
Find the limit of $\lim\limits_{(x,y)\to (0,0)} \frac{x^2y^2}{x^2y^2+(x-y)^2}$
26617
Minimum value of $ f(x,y,z)=\left(x+\frac{1}{y}\right)^2+\left(y+\frac{1}{z}\right)^2+\left(z+\frac{1}{x}\right)^2. $
65235
Show that if $\sum_na_n=\infty$ and $a_n\downarrow 0$ then $\sum\limits_n\min(a_{n},\frac{1}{n})=\infty$
35169
Finding the limit of $\left(\frac{n}{n+1}\right)^n$
102425
Limit $ a_{n+1} = \frac{1}{3}(2a_n + \frac{5}{a_n^{2}}), a_1 > 0 $
16749
Let $A_i= \left \{...,-2,-1,0,1,...,i \right\}$. Find $\bigcup_{i=1}^{n} A_i$ and $\bigcap_{i=1}^{n} A_i$
64329
Limit of the recursive sequence $a_{n+1} = \frac{1}{2}(a_n + \frac{p}{a_n})$
123970
Find $L=\lim \limits_{n\to \infty}\sqrt[n]{x^n+y^n+z^n}$
82775
if $a>1$, Prove that $\lim a^{1\over n}=1$
78393
Find the limit $\lim_{n\to\infty} \frac{x_1 y_n + x_2 y_{n-1} + \cdots + x_n y_1}{n}$
50019
Prove $0$ is a partial limit of $a_n$
130543
If $a_n = \sum\limits_{r=0}^n \binom{n}{r} b_r$, prove $(-1)^n b_n = \sum\limits_{s=0}^n \binom{n}{s} (-1)^s a_s$
79276
Find $\min(\operatorname{trace}(AA^T))$ for invertible $A_{n\times n}$