Sum of numerators divided by sum of denominators $\leq$ the maximum fraction
20040
shorter proof of generalized mediant inequality?
2708
Inequality ${n \choose k} \leq \left(\frac{en}{ k}\right)^k$
155005
How to show $\sum_{k=n}^\infty{\frac{1}{k!}} \leq \frac{2}{n!}$
10902
Showing that $ \prod\limits_{i=0}^{n} {n \choose i}\leq(\frac{2^n-2}{n-1})^{n-1} $
45361
Checking the consistency and Bias of $\frac{\sum X_i +\sqrt{n}/2}{n+\sqrt{n}}$
17375
When is the limit of a sum equal to the sum of limits?
22274
Partitioning a natural number $n$ in order to get the maximum product sequence of its addends
149700
Prove that $\frac{a_1^2}{a_1+a_2}+\frac{a_2^2}{a_2+a_3}+ \cdots \frac{a_n^2}{a_n+a_1} \geq \frac12$
102420
How to prove that adding $n$ to the numerator and denominator will move the resultant fraction close to $1$?
24469
Prove $ 2<(1+\frac{1}{n})^{n}$
118161
Proof of dividing fractional expressions
15441
Show $\frac{1}{4}\leq \mu(A\cap B \cap C)$
86051
Find the sum of reciprocals of divisors given the sum of divisors
93427
Show that $\sum_{i=1}^{n} \frac {a_i}{1+a-a_i} + \prod_{i=1}^{n} {(1-a_i)} \leq 1$
154085
$\sum a_i \ln(b_i) \leq \sum a_i \ln(a_i)$ with $\sum a_i = \sum b_i = 1$
58629
Show that the $\max{ \{ x,y \} }= \frac{x+y+|x-y|}{2}$.
24683
For i.i.d. $\{X_n\}$ proving $\frac1n\max\limits_{1\leqslant k\leqslant n}|X_k|\xrightarrow{\mathrm{a.s.}}0\Leftrightarrow E(|X_1|)<+∞$