Question

Prove sum of combinations

score 1.2k · Answer 1 · 2014-11-21 00:32:30

1.2k

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Prove sum of combinations

Published on 21 Nov 2014 - 0:32

score 846 · Answer 2 · 2026-03-28 06:30:21

846

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Induction proof for Fibonacci numbers

Published on 28 Mar 2026 - 6:30

score 117 · Answer 3 · 2014-11-21 04:25:48

117

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Prove that $ \frac{1}{2!} + \frac{2}{3!} + \frac{3}{4!}+\cdots + \frac{n}{(n+1)!} = 1 - \frac{1}{(n+1)!}$ for $n\in \mathbb N$

Published on 21 Nov 2014 - 4:25

score 62 · Answer 4 · 2026-04-01 18:57:42

62

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Show that $7\mid 2^{3n} -1 \,\,\,\forall n\in \mathbb N^+$

Published on 01 Apr 2026 - 18:57

score 105 · Answer 5 · 2014-11-21 11:55:01

105

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Showing that a sequence (defined in terms of the previous sequence term) is increasing and bounded above

Published on 21 Nov 2014 - 11:55

score 605 · Answer 6 · 2014-11-21 15:41:24

605

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How to prove $0 < a_n < 1$ by induction

Published on 21 Nov 2014 - 15:41

score 242 · Answer 7 · 2014-11-21 19:32:34

242

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Induction Proofs - Mathematics

Published on 21 Nov 2014 - 19:32

score 209 · Answer 8 · 2014-11-21 19:54:49

209

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Prove that $(1+2+3+\cdots + n)^2 = 1^3+2^3+3^3+\cdots + n^3$ for every $n \in \mathbb{N}$

Published on 21 Nov 2014 - 19:54

score 120 · Answer 9 · 2026-04-05 21:30:28

120

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Induction Proof that $\sum_{i=0}^n 3^{n-i} {n \choose i} = \sum_{i=0}^n (-1)^i 5^{n-i} {n \choose i}$

Published on 05 Apr 2026 - 21:30

score 142 · Answer 10 · 2014-11-22 12:00:00

142

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Using mathematical induction to show that for any $n\ge 2$ then $\prod_{i=2}^n\bigl(1-\frac{1}{i^2}\bigr)=\frac{n+1}{2 n}$

Published on 22 Nov 2014 - 12:00

score 2.8k · Answer 11 · 2014-11-23 09:54:05

2.8k

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Inequalities - proof by induction that $n^2 \leq n!$ for $n\geq 4$

Published on 23 Nov 2014 - 9:54

score 126 · Answer 12 · 2014-11-23 19:13:02

126

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Prove that if there are $2n$ points and $n^2+1$ straight lines connecting them, then there are at least $n$ triangles in this shape.

Published on 23 Nov 2014 - 19:13

score 306 · Answer 13 · 2026-03-30 02:11:32

306

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Looking for a way to improve my inductive proof of a statement derived by Rolle's Theorem

Published on 30 Mar 2026 - 2:11

score 11.4k · Answer 14 · 2026-03-28 06:31:01

11.4k

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Prove that $F(1) + F(3) + F(5) + ... + F(2n-1) = F(2n)$

Published on 28 Mar 2026 - 6:31

score 103 · Answer 15 · 2026-04-05 17:58:42

103

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Show that it is the solution of the recurrence

Published on 05 Apr 2026 - 17:58

List Question

Prove sum of combinations

Induction proof for Fibonacci numbers

Prove that $ \frac{1}{2!} + \frac{2}{3!} + \frac{3}{4!}+\cdots + \frac{n}{(n+1)!} = 1 - \frac{1}{(n+1)!}$ for $n\in \mathbb N$

Show that $7\mid 2^{3n} -1 \,\,\,\forall n\in \mathbb N^+$

Showing that a sequence (defined in terms of the previous sequence term) is increasing and bounded above

How to prove $0 < a_n < 1$ by induction

Induction Proofs - Mathematics

Prove that $(1+2+3+\cdots + n)^2 = 1^3+2^3+3^3+\cdots + n^3$ for every $n \in \mathbb{N}$

Induction Proof that $\sum_{i=0}^n 3^{n-i} {n \choose i} = \sum_{i=0}^n (-1)^i 5^{n-i} {n \choose i}$

Using mathematical induction to show that for any $n\ge 2$ then $\prod_{i=2}^n\bigl(1-\frac{1}{i^2}\bigr)=\frac{n+1}{2 n}$

Inequalities - proof by induction that $n^2 \leq n!$ for $n\geq 4$

Prove that if there are $2n$ points and $n^2+1$ straight lines connecting them, then there are at least $n$ triangles in this shape.

Looking for a way to improve my inductive proof of a statement derived by Rolle's Theorem

Prove that $F(1) + F(3) + F(5) + ... + F(2n-1) = F(2n)$

Show that it is the solution of the recurrence

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