Let $a_1,a_2,\ldots,a_n$ be positive real numbers.Prove that...
76638
Find the limit $ \lim_{n \to \infty}\left(\frac{a^{1/n}+b^{1/n}+c^{1/n}}{3}\right)^n$
5927
How to prove $a_1^m + a_2^m + \cdots + a_n^m \geq \frac{1}{a_1} + \frac{1}{a_2} + \cdots + \frac{1}{a_n}$
16660
Prove that any positive number has an $n$th root
145397
How to prove that for every $i$, $a_i = i$
139383
Prove that $\tau(2^n-1) \geq \tau(n)$ for all positive integers $n$.
141102
If $a,b,c$ are positive integers, with $a^2+b^2-ab=c^2$ prove that $(a-b)(b-c)\le0$.
71012
If $a, b$ are positive integers such that $a|b^2, b^2|a^3,....$ then $a=b$.
15599
Given that a,b,c are distinct positive real numbers, prove that (a + b +c)( 1/a + 1/b + 1/c)>9
88598
Property of $\{0^n, 1^n, \ldots\}$
18477
$(W_1+W_2+\cdots+W_n)^a \leq W_1^a +\cdots + W_n^a$ for $n$ integer, $n\geq 2$, $W\gt 0$ and $a$ constant, real, $0\lt a\lt 1$
64320
Prove that if $0<a<Pr(A)$ then there exists $B\subset A$ such that $Pr(B)=a$
31544
How to prove that this polynomial is larger than another for positive reals?
122942
Prove that if $\sum |a_{n}|$ converges then $\sum a_{n}^{2}$ converges
68771
Assume that $ 1a_1+2a_2+\cdots+na_n=1$, where the $a_j$ are real numbers.
80827
Let $A$ be a nonempty subset of $\mathbb{R}$. Prove...
54900
How to prove $|\sum_{i=1}^n a_i|\le \sqrt{n} \sqrt{\sum_{i=1}^n a_i^2}$
114043
Prove the existence of a real number satisfying a property