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Help me solve this mathematical induction ( 1 * 1! + 2 * 2! + ... + (n - 1) * (n - 1)! = n! - 1 where n > 0)

score 72 · Answer 1 · 2026-04-16 06:40:03

72

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Help me solve this mathematical induction ( 1 * 1! + 2 * 2! + ... + (n - 1) * (n - 1)! = n! - 1 where n > 0)

Published on 16 Apr 2026 - 6:40

score 1k · Answer 2 · 2026-05-07 12:47:10

1k

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Is there any formal problem that cannot be proven using mathematical induction?

Published on 07 May 2026 - 12:47

score 43 · Answer 3 · 2026-04-12 17:12:26

43

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Mathematical induction by inequality

Published on 12 Apr 2026 - 17:12

score 116 · Answer 4 · 2026-04-29 12:42:54

116

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Induction with a recursive sequence

Published on 29 Apr 2026 - 12:42

score 6.5k · Answer 5 · 2026-04-14 22:10:22

6.5k

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Questions on how to prove that a set of connectives is NOT functionally complete

Published on 14 Apr 2026 - 22:10

score 92 · Answer 6 · 2026-04-14 23:46:57

Using induction on $k$, show that $\sum\limits^{n-1}_{i=1} i^k \le \frac{n^{k+1}}{k+1} \le \sum\limits^n_{i=1} i^k$

score 183 · Answer 7 · 2026-04-30 22:54:10

183

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Use induction to show that a truth assignment on $\Gamma\cup\Lambda$ satisfies all theorem from $\Gamma$

Published on 30 Apr 2026 - 22:54

score 728 · Answer 8 · 2026-04-09 08:31:13

728

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Induction on an if-then statement

Published on 09 Apr 2026 - 8:31

score 561 · Answer 9 · 2026-05-10 12:34:55

561

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Prove by induction that the direct sum of subspaces of a vector space...

Published on 10 May 2026 - 12:34

score 163 · Answer 10 · 2026-04-13 14:43:48

163

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Prove by induction that $(k + 2)^{k + 1} \leq (k+1)^{k +2}$

Published on 13 Apr 2026 - 14:43

score 134 · Answer 11 · 2026-03-25 11:06:25

134

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Axiomless proof of induction and well ordering principle

Published on 25 Mar 2026 - 11:06

score 73 · Answer 12 · 2026-05-03 00:20:22

73

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Proof $n \geq 3\hspace{0.5cm} \sum\limits_{k=1}^{n-2}{n-k\choose 2}={n\choose 3}$

Published on 03 May 2026 - 0:20

score 4.3k · Answer 13 · 2026-04-29 12:51:11

4.3k

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Prove that $1 · 1! + 2 · 2! + … + n · n! = (n + 1)! − 1$ via mathematical induction?

Published on 29 Apr 2026 - 12:51

score 208 · Answer 14 · 2026-04-16 13:58:16

208

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$a_n $ is a positive integer for any $n\in \mathbb {N} $.

Published on 16 Apr 2026 - 13:58

score 251 · Answer 15 · 2026-04-16 09:34:24

251

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How can I prove that: $55...5 = \frac{5}{9} (10^n -1)$

Published on 16 Apr 2026 - 9:34

List Question

Help me solve this mathematical induction ( 1 * 1! + 2 * 2! + ... + (n - 1) * (n - 1)! = n! - 1 where n > 0)

Is there any formal problem that cannot be proven using mathematical induction?

Mathematical induction by inequality

Induction with a recursive sequence

Questions on how to prove that a set of connectives is NOT functionally complete

Using induction on $k$, show that $\sum\limits^{n-1}_{i=1} i^k \le \frac{n^{k+1}}{k+1} \le \sum\limits^n_{i=1} i^k$

Use induction to show that a truth assignment on $\Gamma\cup\Lambda$ satisfies all theorem from $\Gamma$

Induction on an if-then statement

Prove by induction that the direct sum of subspaces of a vector space...

Prove by induction that $(k + 2)^{k + 1} \leq (k+1)^{k +2}$

Axiomless proof of induction and well ordering principle

Proof $n \geq 3\hspace{0.5cm} \sum\limits_{k=1}^{n-2}{n-k\choose 2}={n\choose 3}$

Prove that $1 · 1! + 2 · 2! + … + n · n! = (n + 1)! − 1$ via mathematical induction?

$a_n $ is a positive integer for any $n\in \mathbb {N} $.

How can I prove that: $55...5 = \frac{5}{9} (10^n -1)$

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