New posts in induction

How to understand if task on graph-theory has analytical solution?

combinatorics graph-theory induction extremal-graph-theory

Odd Binomial Coefficients?

elementary-number-theory induction binomial-coefficients parity

How do I prove that any chessboard of size $n \times 3$, where n is even and $n \geq 10$, has a closed knight's tour?

Fiboncacci theorem: Proof by induction that $F_{n} \cdot F_{n+1} - F_{n-2}\cdot F_{n-1}=F_{2n-1}$

induction fibonacci-numbers

Help with graph induction question?

graph-theory induction

Proof of equality $\sum_{k=0}^{m}k^n = \sum_{k=0}^{n}k!{m+1\choose k+1} \left\{^n_k \right\} $ by induction

summation induction binomial-coefficients

Proof by induction on Fibonacci numbers: show that $f_n\mid f_{2n}$

elementary-number-theory induction divisibility fibonacci-numbers

Solving Induction $\prod\limits_{i=1}^{n-1}\left(1+\frac{1}{i}\right)^{i} = \frac{n^{n}}{n!}$

induction exponentiation factorial products

Irrationality of $\sqrt 2$ using induction

elementary-number-theory induction

Use Principle of Mathematical Induction to show that for all $n\:\in \mathbb{N}$, $a_n=2^{n+2}\cdot 5^{2n+1}+3^{n+2}\cdot 2^{2n+1}$ is divisible by 19

Consistency of Peano axioms (Hilbert's second problem)?

logic induction incompleteness natural-numbers

Prove $\frac{1}{2} + \cos(x) + \cos(2x) + \dots+ \cos(nx) = \frac{\sin(n+\frac{1}{2})x}{2\sin(\frac{1}{2}x)}$ for $x \neq 0, \pm 2\pi, \pm 4\pi,\dots$

sequences-and-series proof-writing induction

Prove $3|n(n+1)(n+2)$ by induction

elementary-number-theory induction divisibility

Prove by mathematical induction that $n^3 - n$ is divisible by $3$ for all natural number $n$

elementary-number-theory induction divisibility

Proving sum of series $\frac{1}{1\cdot 3}+\frac{1}{3\cdot 5}+\frac{1}{5\cdot 7}+\dots+\frac{1}{(2n-1)(2n+1)}=\frac{n}{2n+1}$

How to prove $\sin x+\frac{\sin 2x}{2}+\frac{\sin 3x}{3}+\cdots$ is positive? [duplicate]

real-analysis inequality induction

Prove that $\sqrt{n} \le \sum_{k=1}^n \frac{1}{\sqrt{k}} \le 2 \sqrt{n} - 1$ is true for $n \in \mathbb{N}^{\ge 1}$

inequality induction problem-solving natural-numbers

Induction Proof: Formula for Sum of n Fibonacci Numbers

induction proof-writing problem-solving fibonacci-numbers

Prove by induction that for $n ≥ 3, 4^{n} > 5n^{2}+ n.$

discrete-mathematics induction

Prove that any palindrome with an even number of digits is divisible by 11

number-theory induction palindrome