New posts in induction

Solve by induction: $n!>(n/e)^n$

inequality induction factorial

Simplifying the product $\prod\limits_{k=2}^n \left(1-\frac1{k^2}\right)$ [duplicate]

sequences-and-series induction products

Prove that the elements of sequences $(a_n),(b_n)$ are rational numbers such that $a_n<\sqrt{2}<b_n=a_n+2^{-n}$ for all $n \geq 1$ using induction

real-analysis sequences-and-series inequality induction proof-explanation

Prove by induction that $n! > n^2$ [duplicate]

inequality induction factorial

Proof by induction of summation inequality: $1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\dots+\frac1{2^n}\ge 1+\frac{n}2$

inequality summation induction harmonic-numbers

How to prove $\sum^n_{i=1} \frac{1}{i(i+1)} = \frac{n}{n+1}$? [duplicate]

induction summation

Prove $n^2(n^4-1)$ is divisible by 60 using Mathematical Induction.

Guess the formula for $\sum\frac 1{(4n-3)(4n+1)}$ and prove by induction

proof-verification induction

Double induction example: $ 1 + q + q^2 + q^3 + \cdots + q^{n-1} + q^n = \frac {q^{n+1}-1}{q-1} $

elementary-number-theory summation induction geometric-series

Proving a summation inequality with induction

discrete-mathematics inequality proof-verification summation induction

Proof by Induction: Solving $1+3+5+\cdots+(2n-1)$

discrete-mathematics summation induction

Number of bitstrings with $000$ as substring

combinatorics induction permutations fibonacci-numbers

Prove that $(a+1)(a+2)...(a+b)$ is divisible by $b!$ [duplicate]

proof-writing induction divisibility factorial

Proving Inequality using Induction $a^n-b^n \leq na^{n-1}(a-b)$

inequality induction

How to prove $4(n!)>2^{n+2}$ for $ n\geq 4$ with induction [duplicate]

proof-writing induction

Inductive proof of gcd Bezout identity (from Apostol: Math, Analysis 2ed)

number-theory induction proof-explanation gcd-and-lcm

Math Induction Proof: $(1+\frac1n)^n < n$

inequality induction

How to prove that for $a_{n+1}=\frac{a_n}{n} + \frac{n}{a_n}$ , we have $\lfloor a_n^2 \rfloor = n$?

sequences-and-series induction recurrence-relations ceiling-and-floor-functions

For every $n\ge3$ there exists $n$ different integers $a_1,...,a_n$ so that $\frac{1}{a_1}+\frac{1}{a_2}+...+\frac{1}{a_n}=1$

Induction: Prove that $4^{n+1}+5^{2 n - 1}$ is divisible by 21 for all $n \geq 1$.