Prove that if $[.]$ is Greatest integer function then $\left[\frac{[x]}{n}\right]=\left[\frac{x}{n}\right]$
5934
How to prove floor identities?
79836
Proof for $\left\lfloor\frac 1j\left\lfloor\frac nk\right\rfloor\right\rfloor=\left\lfloor\frac n{jk}\right\rfloor$
48891
Show that: lim$_{n\rightarrow \infty}\,f(x_n)=f(\text{lim}_{n \rightarrow \infty} \, x_n)$
61162
Show that $\left(\int_0^1 f(x)\,dx\right)^2\leq2\int_0^1x\, f(x)^2\,dx $
98768
Prove $\left(1+\frac{x}{n}\right)^n < e^x$, where $x$ is any positive real number and $n$ is any positive integer.
49109
Proving $\gcd \left(\frac{a}{\gcd (a,b)},\frac{b}{\gcd (a,b)}\right)=1$
25921
Show that $\left(1+\dfrac{1}{n}\right)^n$ is monotonically increasing
21802
Prove $\sum_{d \leq x} \mu(d)\left\lfloor \frac xd \right\rfloor = 1 $
72694
Proving that $f(x) = g(x)$ for some $x \in [a,b]$ if $f,g$ continuous, $f(a)  g(b)$
126931
Find $f(x)$ such that $f(x)+f\left(\frac{1}{x}\right)=f(x)\cdot f\left(\frac{1}{x}\right)$
13390
Recursive Monotone Decreasing Sequence Proof ${x_{k}} = \frac{1}{2}\left({x_{k-1}+\frac{a}{{x_{k-1}}}}\right)$
136274
$n! \leq \left( \frac{n+1}{2} \right)^n$ via induction
44940
Proving by induction that $1^3 + 2^3 + 3^3 + \ldots + n^3 = \left[\frac{n(n+1)}{2}\right]^2$
105145
Show that $\mathbb{E}\left(\bar{X}_{n}\mid X_{(1)},X_{(n)}\right) = \frac{X_{(1)}+X_{(n)}}{2}$
145423
prove that if $1 \le m \le n$ then $\left(1+\frac1n\right)^m < 1+\frac mn + \left(\frac mn\right)^2$
52858
Find $f$ if $ f(x)+f\left(\frac{1}{1-x}\right)=x $
45742
Prove that ${\left(\frac{x+1}{2}\right)}^{x+1} \leq x^x$