Question

Prove by induction that $a^{m+n} = a^m \times a^n$ and $(a^m)^n = a^{mn}$, for $a \in \mathbb{R}$ and $n, m \in \mathbb{N}$.

score 472 · Answer 1 · 2018-04-18 07:46:55

Prove by induction that $a^{m+n} = a^m \times a^n$ and $(a^m)^n = a^{mn}$, for $a \in \mathbb{R}$ and $n, m \in \mathbb{N}$.

score 1.4k · Answer 2 · 2018-04-18 12:43:46

1.4k

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Integration and Proof by induction

Published on 18 Apr 2018 - 12:43

score 58 · Answer 3 · 2026-03-25 09:26:23

58

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Induction proof: $n! > (\frac{n}{2})^\frac{n}{2}$

Published on 25 Mar 2026 - 9:26

score 1.7k · Answer 4 · 2018-04-18 17:47:18

1.7k

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Proof by induction when there are two cases?

Published on 18 Apr 2018 - 17:47

score 453 · Answer 5 · 2018-04-19 13:44:42

453

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How do I use rule induction to prove this relation?

Published on 19 Apr 2018 - 13:44

score 154 · Answer 6 · 2018-04-19 21:08:23

154

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Use induction to prove $\sum_{i=0}^n i^3 = (\sum_{i=0}^n i)^2$

Published on 19 Apr 2018 - 21:08

score 141 · Answer 7 · 2018-04-20 05:04:42

141

Views

Use the mathematical Induction show that $H_{2^n}\le n+1$

Published on 20 Apr 2018 - 5:04

score 262 · Answer 8 · 2018-04-20 13:09:22

262

Views

Prove that $6$ is a divisor of $n^3 - n$ for all natural numbers.

Published on 20 Apr 2018 - 13:09

score 335 · Answer 9 · 2018-04-20 15:44:36

335

Views

Is it possible to start a proof by induction with a vacuously true statement?

Published on 20 Apr 2018 - 15:44

score 294 · Answer 10 · 2018-04-20 19:37:58

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

score 11.6k · Answer 11 · 2018-04-21 00:46:51

11.6k

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Proof by induction that $2^n+1 \leq 3^n$ for all positive integers $n$

Published on 21 Apr 2018 - 0:46

score 15 · Answer 12 · 2026-03-06 23:21:01

15

Views

induction to m | $n,m \in \mathbb{N} $

Published on 06 Mar 2026 - 23:21

score 101 · Answer 13 · 2018-04-21 16:43:57

101

Views

Proving by induction the explicit form of a recursive sequence.

Published on 21 Apr 2018 - 16:43

score 520 · Answer 14 · 2026-03-25 06:06:47

520

Views

Prove that ${F_{n+1}} = \sum_{k=0}^{n}\binom{n-k}{k}$ where ${F_{n}}$ is n-th Fibonacci number

Published on 25 Mar 2026 - 6:06

score 88 · Answer 15 · 2026-03-25 03:03:42

88

Views

How to show that $a_n=1+1/\sqrt{2}+\cdots+(1/\sqrt{n-1})-2\sqrt{n}$ has an upper bound.

Published on 25 Mar 2026 - 3:03

List Question

Prove by induction that $a^{m+n} = a^m \times a^n$ and $(a^m)^n = a^{mn}$, for $a \in \mathbb{R}$ and $n, m \in \mathbb{N}$.

Integration and Proof by induction

Induction proof: $n! > (\frac{n}{2})^\frac{n}{2}$

Proof by induction when there are two cases?

How do I use rule induction to prove this relation?

Use induction to prove $\sum_{i=0}^n i^3 = (\sum_{i=0}^n i)^2$

Use the mathematical Induction show that $H_{2^n}\le n+1$

Prove that $6$ is a divisor of $n^3 - n$ for all natural numbers.

Is it possible to start a proof by induction with a vacuously true statement?

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

Proof by induction that $2^n+1 \leq 3^n$ for all positive integers $n$

induction to m | $n,m \in \mathbb{N} $

Proving by induction the explicit form of a recursive sequence.

Prove that ${F_{n+1}} = \sum_{k=0}^{n}\binom{n-k}{k}$ where ${F_{n}}$ is n-th Fibonacci number

How to show that $a_n=1+1/\sqrt{2}+\cdots+(1/\sqrt{n-1})-2\sqrt{n}$ has an upper bound.

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