Find all functions $f(x)$ such that $f(x)+f\left(\frac{x-1}{x}\right)=2 x+4$
110704
Find all functions $f$ such that $f(x)+f(\frac{1}{1-x})=x$
14883
Find $\sum_{n=1}^{\infty}$ $\frac{n^{2}}{\left(n+1\right)\left(n+2\right)\left(n+3\right)\left(n+4\right)}$
27809
Find the function equation $f(x+f(y)+yf(x))=y+f(x)+xf(y)$
144445
Functions $f:\mathbb{N}\rightarrow \mathbb{Z}$ such that $\left(m-n\right) \mid \left(f(m)-f(n)\right)$
50606
Find $\sum\limits_{k\, \text{ odd}} \frac{2(k^2-1)}{k^4+k^2+1}$
101743
Find the limit: $\lim \limits_{x \to 1} \left( {\frac{x}{{x - 1}} - \frac{1}{{\ln x}}} \right)$
77071
Solve the functional equation $f(xy) = f(x)f(y) - f(x + y) + 1$ and $f(1) = 2$
69673
Prove that $\left (\frac{a^2 + b^2 +c^2}{a+b+c} \right) ^ {(a+b+c)} > a^a b^b c^c$
106853
Find all functions: $\left ( \int \frac{dx}{f(x)} \right )\left ( \int f(x)dx \right )=c$
45742
Prove that ${\left(\frac{x+1}{2}\right)}^{x+1} \leq x^x$
52858
Find $f$ if $ f(x)+f\left(\frac{1}{1-x}\right)=x $
37976
Find all functions $f$ such that $(x+y)f(x)+f(y^2)=(x+y)f(y)+f(x^2)$
127396
When is $f=\left(\frac{\sqrt{p+4}}{1-p}-1\right)x^5-3x+\ln5$ decreasing $\forall\; x$?
71547
Prove $ 1+\left( 1-\frac{x}{n}\right)+...+\left(1-\frac{x}{n}\right)^{n-1}=\frac{n}{x}\left(1-\left(1-\frac{x}{n}\right)^n\right)$
81799
Examples of functions where $f(ab)=f(a)+f(b)$
26754
Find all continuous functions satisfying $\int_0^xf=(f(x))^2+C$ for some constant $C \neq 0$.
137614
$\left|\frac{x}{|x|}-\frac{y}{|y|}\right|\leq |x-y|$, for $|x|, |y|\geq 1$?