Question

$\sum_{i=0}^n \frac{1}{(i+3)(i+4)} = \frac{n}{4(n+4)}$ (prove by induction)

score 61 · Answer 1 · 2018-03-06 17:44:08

61

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$\sum_{i=0}^n \frac{1}{(i+3)(i+4)} = \frac{n}{4(n+4)}$ (prove by induction)

Published on 06 Mar 2018 - 17:44

score 362 · Answer 2 · 2018-03-06 21:42:17

362

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Proof by induction (Chinese remainder theorem?)

Published on 06 Mar 2018 - 21:42

score 198 · Answer 3 · 2018-03-06 22:57:48

198

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Proof help: Induction ( $ 1/ \sqrt1 + 1/\sqrt2 +....+1/\sqrt{n}$ $< \sqrt{n}$ ) for $n>1$

Published on 06 Mar 2018 - 22:57

score 610 · Answer 4 · 2026-03-25 02:57:06

610

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Proof with induction on $n$ so that the complete graph $K_n$ has $(n-1)!$ hamilton cycle for all $n \geq 3$.

Published on 25 Mar 2026 - 2:57

score 1.2k · Answer 5 · 2018-03-07 18:34:29

1.2k

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Prove that $3^{2n-1} + 2^{n+1}$ is always a multiple of $7$.

Published on 07 Mar 2018 - 18:34

score 192 · Answer 6 · 2018-03-07 20:49:21

192

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Prove $3^{2n}-5$ is a multiple of $4$

Published on 07 Mar 2018 - 20:49

score 72 · Answer 7 · 2026-03-22 00:47:03

72

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Preserving Parity through substitution

Published on 22 Mar 2026 - 0:47

score 381 · Answer 8 · 2018-03-08 22:04:13

I am having trouble understanding how to prove that the sum of the first $n$ positive even integers is $n^2 + n$ using strong induction.

score 179 · Answer 9 · 2018-03-09 00:38:39

179

Views

Is function f a bijection? Why or why not? How to prove by induction?

Published on 09 Mar 2018 - 0:38

score 88 · Answer 10 · 2026-03-24 23:52:53

88

Views

Prove a recursive sequence using induction

Published on 24 Mar 2026 - 23:52

score 85 · Answer 11 · 2018-03-09 22:02:16

85

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Induction $24|n^{6}-3n^{5}+6n^{4}-7n^{3}+5n^{2}-2n$

Published on 09 Mar 2018 - 22:02

score 1.5k · Answer 12 · 2026-03-22 16:04:58

1.5k

Views

What happened here at the proof of associative law for addition?

Published on 22 Mar 2026 - 16:04

score 789 · Answer 13 · 2018-03-12 00:33:16

789

Views

Weak induction: $\log(n!) < n\log(n)$

Published on 12 Mar 2018 - 0:33

score 166 · Answer 14 · 2026-03-25 12:13:18

166

Views

Variations in the Statement of Strong Induction: Equivalent or Different?

Published on 25 Mar 2026 - 12:13

score 94 · Answer 15 · 2026-03-25 04:43:52

94

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Is it to say that whenever we use mathematical induction, we're inevitably admitting Peano axioms for $\Bbb N$ indeed?

Published on 25 Mar 2026 - 4:43

List Question

$\sum_{i=0}^n \frac{1}{(i+3)(i+4)} = \frac{n}{4(n+4)}$ (prove by induction)

Proof by induction (Chinese remainder theorem?)

Proof help: Induction ( $ 1/ \sqrt1 + 1/\sqrt2 +....+1/\sqrt{n}$ $< \sqrt{n}$ ) for $n>1$

Proof with induction on $n$ so that the complete graph $K_n$ has $(n-1)!$ hamilton cycle for all $n \geq 3$.

Prove that $3^{2n-1} + 2^{n+1}$ is always a multiple of $7$.

Prove $3^{2n}-5$ is a multiple of $4$

Preserving Parity through substitution

I am having trouble understanding how to prove that the sum of the first $n$ positive even integers is $n^2 + n$ using strong induction.

Is function f a bijection? Why or why not? How to prove by induction?

Prove a recursive sequence using induction

Induction $24|n^{6}-3n^{5}+6n^{4}-7n^{3}+5n^{2}-2n$

What happened here at the proof of associative law for addition?

Weak induction: $\log(n!) < n\log(n)$

Variations in the Statement of Strong Induction: Equivalent or Different?

Is it to say that whenever we use mathematical induction, we're inevitably admitting Peano axioms for $\Bbb N$ indeed?

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