New posts in Power Series

Matrix Geometric Series

Summation problem: $f(x)=1+\sum_{n=1}^{\infty}\frac{x^n}{n}$

Prove $\sum_{i=0}^n (-1)^{n-i} \binom{n+1}{i} (i+1)^n = (n+2)^n$

Integral $\int_0^\frac{\pi}{2} \arcsin(\sqrt{\sin x}) dx$

A direct proof for $\int_0^x \frac{- x \ln(1-u^2)}{u \sqrt{x^2-u^2}} \, \mathrm{d} u = \arcsin^2(x)$

Physical intuition for the solution to $y' = y$.

Proving finite sum identity

What is $\lim_{x\to1^{-}} (1-x)\left(\sum_{i=0}^{\infty} x^{i^2}\right)^{2}$?

$f(z)= \frac{z}{1-e^{-z}}$ $\Leftrightarrow$ $\forall n \ge 0$ and $n\in\mathbb{Z}$, coefficient of $z^n$ in $f^{n+1}(z)$ is $1$.

Third degree Taylor series of $f(x) = e^x \cos{x} $