New posts in faq

Proving $1^3+ 2^3 + \cdots + n^3 = \left(\frac{n(n+1)}{2}\right)^2$ using induction

algebra-precalculus induction summation faq

Determinant of a rank $1$ update of a scalar matrix, or characteristic polynomial of a rank $1$ matrix

linear-algebra matrices determinant characteristic-polynomial faq

Values of $\sum_{n=0}^\infty x^n$ and $\sum_{n=0}^N x^n$

sequences-and-series algebra-precalculus summation faq geometric-progressions

Overview of basic facts about Cauchy functional equation

functional-equations online-resources faq

How to prove: if $a,b \in \mathbb N$, then $a^{1/b}$ is an integer or an irrational number?

number-theory radicals faq rationality-testing

Proof of the hockey stick/Zhu Shijie identity $\sum\limits_{t=0}^n \binom tk = \binom{n+1}{k+1}$

combinatorics summation combinations binomial-coefficients faq

$\sqrt{c+\sqrt{c+\sqrt{c+\cdots}}}$, or the limit of the sequence $x_{n+1} = \sqrt{c+x_n}$

calculus sequences-and-series limits faq nested-radicals

Different methods to compute $\sum\limits_{k=1}^\infty \frac{1}{k^2}$ (Basel problem)

sequences-and-series fourier-analysis big-list transcendental-numbers faq

Modular exponentiation by hand ($a^b\bmod c$)

elementary-number-theory modular-arithmetic exponentiation faq

How can I evaluate $\sum_{n=0}^\infty(n+1)x^n$?

sequences-and-series convergence-divergence power-series geometric-series faq