Question

Proof via induction $1\cdot3 + 2\cdot4 + 3\cdot5 + \cdots + n(n+2) = \frac{n(n+1)(2n+7)}{6}$

score 239 · Answer 1 · 2014-05-07 18:14:08

239

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Proof via induction $1\cdot3 + 2\cdot4 + 3\cdot5 + \cdots + n(n+2) = \frac{n(n+1)(2n+7)}{6}$

Published on 07 May 2014 - 18:14

score 22.4k · Answer 2 · 2026-03-27 04:38:08

22.4k

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Prove the commutativity property of addition of natural numbers by induction

Published on 27 Mar 2026 - 4:38

score 683 · Answer 3 · 2014-05-09 08:55:57

683

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Summation Induction when lower limit is not 1

Published on 09 May 2014 - 8:55

score 45 · Answer 4 · 2014-05-10 05:35:40

45

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Induction proof $2^{n+1}-1$ when n is 50

Published on 10 May 2014 - 5:35

score 59 · Answer 5 · 2014-05-11 04:41:34

59

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Using induction to prove an equation

Published on 11 May 2014 - 4:41

score 2.1k · Answer 6 · 2014-05-11 13:00:49

2.1k

Views

Prove that $n = 2a + 3b$.

Published on 11 May 2014 - 13:00

score 56 · Answer 7 · 2014-05-11 15:25:29

56

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Inductive step assumption for all numbers up to $n$

Published on 11 May 2014 - 15:25

score 3.4k · Answer 8 · 2014-05-11 16:58:55

3.4k

Views

Proof by induction using logarithms

Published on 11 May 2014 - 16:58

score 95 · Answer 9 · 2026-03-27 19:30:34

95

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Induction: prove $2n^2 < 10\cdot n!$

Published on 27 Mar 2026 - 19:30

score 3.4k · Answer 10 · 2014-05-14 03:04:21

3.4k

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Induction: the complement A1 U A2 … U An is the intersection of Ac 1, Ac 2, …, Ac n

Published on 14 May 2014 - 3:04

score 1.5k · Answer 11 · 2014-05-14 03:30:20

1.5k

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Proof by induction: Prove that $6$ divides $9^n - 3^n$

Published on 14 May 2014 - 3:30

score 14.7k · Answer 12 · 2014-05-14 13:10:01

14.7k

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$6^{(n+2)} + 7^{(2n+1)}$ is divisible by $43$ for $n \ge 1$

Published on 14 May 2014 - 13:10

score 65 · Answer 13 · 2026-03-25 23:37:35

65

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Lemma about a prime ideal in a commutative ring with identity

Published on 25 Mar 2026 - 23:37

score 1.1k · Answer 14 · 2026-04-03 03:17:14

1.1k

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Integral of $\sin^n(x)$, recurrence relation, some properties

Published on 03 Apr 2026 - 3:17

score 143 · Answer 15 · 2026-03-26 12:37:46

143

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Show that $b_n > b_{n-1}$ where $\frac{a_n}{b_n}$ are the n:th harmonic number

Published on 26 Mar 2026 - 12:37

List Question

Proof via induction $1\cdot3 + 2\cdot4 + 3\cdot5 + \cdots + n(n+2) = \frac{n(n+1)(2n+7)}{6}$

Prove the commutativity property of addition of natural numbers by induction

Summation Induction when lower limit is not 1

Induction proof $2^{n+1}-1$ when n is 50

Using induction to prove an equation

Prove that $n = 2a + 3b$.

Inductive step assumption for all numbers up to $n$

Proof by induction using logarithms

Induction: prove $2n^2 < 10\cdot n!$

Induction: the complement A1 U A2 … U An is the intersection of Ac 1, Ac 2, …, Ac n

Proof by induction: Prove that $6$ divides $9^n - 3^n$

$6^{(n+2)} + 7^{(2n+1)}$ is divisible by $43$ for $n \ge 1$

Lemma about a prime ideal in a commutative ring with identity

Integral of $\sin^n(x)$, recurrence relation, some properties

Show that $b_n > b_{n-1}$ where $\frac{a_n}{b_n}$ are the n:th harmonic number

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