Prove that there exists a $z \in Z(G)$ such that $yx = zxy$.
Does $\sum_{n=2}^{\infty} \frac{(-1)^n}{\ln(n)}$ have a closed form
Expectation $E[\frac{X_1 + X_2 + … + X_k}{X_1 + X_2 + … + X_n}]$, where $k < n$
Let $Y_1, \ldots , Y_n$ be independent with $Y_k \sim U(0,1).$ If $S_n=\Sigma_k kY_k$, show that $4S_n/n^2$ converges in distribution to $1.$
Is this statement about field extensions true or false
Prove that $X_1\cup X_2$ is path connected if and only if both $X_1$ and $X_2$ are path connected
Find the generating function of $f(n) = \sum_{k = 0}^n \binom{n}{k} (-1)^{n-k}C_{k}$
Show compactification of positive real plane is homeomorphic to $\Bbb R \Bbb P^2$
How to prove that f does not depend on y
Suppose that $X$ is Hausdorff. Show that $X$ is locally path connected.