Show that $\Sigma_{j=0}^n z^j=\frac{1-z^{n+1}}{1-z}$
2678
Values of $\sum_{n=0}^\infty x^n$ and $\sum_{n=0}^N x^n$
101286
How show that $|a_{n}-1|\le c\lambda ^n,\lambda\in (0,1)$
78712
Prove that $\frac{1}{\sin^2 z } = \sum\limits_{n= -\infty} ^ {+\infty} \frac{1}{(z-\pi n)^2} $
102553
How to show that $f(z) = f(i)$
120985
Prove that $\mathrm{Res}[f/g,z_0]=\frac{f(z_0)}{g'(z_0)}$
67820
Showing that $(A_{ij})=\left(\frac1{1+x_i+x_j}\right)$ is positive semidefinite
105882
Prove that the sequence with $T(0)=1$ and $T(n) = 1 + \sum_{j=0}^{n-1}T(j)$ is given by $T(n)=2^n$
127169
Show that the zeros of $\sum_{k=1}^n kz^{k-1}$ are inside the unit disc
103851
Show that $\frac{xy}{z} + \frac{xz}{y} + \frac{yz}{x} \geq x+y+z $ by considering homogeneity
37283
Show that $\frac{X-\mu}{\sigma}\sim N(0,1)$ using moment functions
60230
Prove that $\frac{1+\sin\theta+i\cos\theta}{1+\sin\theta-i\cos\theta}=\sin\theta+i\cos\theta$
121661
Evaluating the sum $\Sigma \, \frac{1}{k(k+p)}$
89136
How prove this $\sum_{k=1}^{2^{n-1}}\sigma{(2^n-2k+1)}\sigma{(2k-1)}=8^{n-1}$
20317
Proving $\sum_{k=1}^{n}{(-1)^{k+1} {{n}\choose{k}}\frac{1}{k}=H_n}$
112329
Show that $d(z,a)=|\frac{z-a}{1-\overline{a}z}|$ is a metric on the unit disk
53266
Show that $R/I\otimes_R R/J\cong R/(I+J)$
44928
Show $\sum_n \frac{z^{2^n}}{1-z^{2^{n+1}}} = \frac{z}{1-z}$