New posts in induction

Prove that $a_1+\cdots+a_n \geq n$ if $a_1$, $a_2$, ... $a_n$ are positive real numbers and their product is $1$

calculus sequences-and-series induction

How to prove $(1+q)^n \geq1+qn$ for all $\mathbb{N}$ with $q>0$

discrete-mathematics inequality induction

How to prove $n < \left(1+\frac{1}{\sqrt{n}}\right)^n$

inequality proof-verification induction

Mathematical induction for inequalities: $\frac1{n+1} + \frac1{n+2} + \cdots +\frac1{3n+1} > 1$

inequality summation induction harmonic-numbers

If a plane is divided by $n$ lines, then it is possible to color the regions formed with only two colors.

geometry discrete-mathematics induction

Prove that at a party with at least two people, there are two people who know the same number of people...

logic discrete-mathematics induction pigeonhole-principle

Why can mathematical induction only be used with natural numbers?

Prove that $\log(x) < x$ for $x > 0$, $x\in \mathbb{N}$.

Showing that the sequence $a_{n+3}=5a^6_{n+2}+3a^3_{n+1}+a^2_n$, with $a_1=2019$, $a_2=2020$, $a_3=2021$, contains no numbers of the form $m^6$

algebra-precalculus induction contest-math

From $n=2$ to $n$-ary Euclid lemma $\ p\mid a_1\cdots a_n\Rightarrow\ p\mid a_1\,$ or $\,\cdots\, p\mid a_n$

elementary-number-theory induction

demonstration by induction: $(1+a)^n ≥1+an$

Use an induction argument to prove that for any natural number $n$, the interval $(n,n+1)$ does not contain any natural number.

induction natural-numbers

Proof by induction; $a^n$ divides $b^n$ implies $a$ divides $b$

number-theory elementary-number-theory proof-writing induction

Proving a combinatorics equality: $\binom{r}{r} + \binom{r+1}{r} + \cdots + \binom{n}{r} = \binom{n+1}{r+1}$

combinatorics summation induction binomial-coefficients

Alternate proof that for every natural number $n,\ \left\lfloor\left(\frac{7+\sqrt{37}}{2}\right)^n\right\rfloor$ is divisible by $3$

elementary-number-theory recurrence-relations induction

For $n \geq 2$, prove that $(1- \frac{1}{4})(1- \frac{1}{9})(1- \frac{1}{16})...(1- \frac{1}{n^2}) = \frac{n+1}{2n}$

Showing $1+2+\cdots+n=\frac{n(n+1)}{2}$ by induction (stuck on inductive step)

summation induction

Prove that $1 + 4 + 7 + · · · + 3n − 2 = \frac {n(3n − 1)}{2}$

discrete-mathematics summation induction arithmetic-progressions

Prove by induction: $n! \ge 2^{(n-1)}$ for any $n \ge 1$ [duplicate]

discrete-mathematics induction exponential-function factorial

Proving by induction: $2^n > n^3 $ for any natural number $n > 9$ [duplicate]

inequality induction