Let $X=\{x|x=1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{n}, n\in \mathbb{N}\}$. Find $X \cap \mathbb{N}$
46946
Is there an elementary proof that $\sum \limits_{k=1}^n \frac1k$ is never an integer?
82170
Solve $x = \frac{1}{2}\tan(x)$
9217
Find $n$ such that $x^2 + x + 1$ is a factor of $(x+1)^n - x^n - 1$.
76527
If $x_{m+n} \le x_n+x_m$, then $\lim x_n/n$ exists and is equal to $\inf x_n/n$
63750
let $f(\frac{x}{3})+f(\frac{2}{x})=\frac{4}{x^2}+\frac{x^2}{9}-2$ then find $f(x)$
19561
Why is $\frac{1}{\frac{1}{X}}=X$?
60456
Find the power series of $f(x)=\frac{1}{x^2+x+1}$
41645
Checking my understanding: $1 - 1 + 1 - 1 + 1 - ... = \frac{1}{2}$
99933
Determine whether $(x_n)$ converges if $x_1= a , x_{n+1} = x_n+\frac{1}{x_n}$ for $n \in \mathbb{N}$
106013
Given $f(x) = x + |x|$ for what values of $x$ is $f$ differentiable
126931
Find $f(x)$ such that $f(x)+f\left(\frac{1}{x}\right)=f(x)\cdot f\left(\frac{1}{x}\right)$
133398
$g(x)=\sum_{n=0}^{\infty} \lceil {\frac{n+1}{2}} \rceil x^n$, find $g(\frac{1}{3})$
64457
Prove:$|x-1|+|x-2|+|x-3|+\cdots+|x-n|\geq n-1$
16774
If $x,y,z\in\mathbb R\setminus \{1\}$ and $xyz=1$, prove that $\frac{x^2}{(x-1)^2}+\frac{y^2}{(y-1)^2}+\frac{z^2}{(z-1)^2}\ge 1$.
34349
Prove that $\frac{1}{1+x_1}+\frac{1}{1+x_2}+\cdots+\frac{1}{1+x_n} \geq \frac{n}{\sqrt[n]{x_1x_2\cdots x_n}+1}$
114212
How to use Mathematical Induction to prove $\frac{1}{1 \cdot 2} + \frac{1}{2 \cdot 3} + \cdots + \frac{1}{n(n + 1)} = \frac{n}{n + 1}$?
14968
How $\frac{1}{n}\sum_{i=1}^n X_i^2 - \bar X^2 = \frac{\sum_{i=1}^n (X_i - \bar X)^2}{n}$