Question

How would you prove that via induction? $\sum_{k=1}^{n}k! \cdot k= (n+1)! -1$

score 131 · Answer 1 · 2016-09-07 19:00:34

131

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How would you prove that via induction? $\sum_{k=1}^{n}k! \cdot k= (n+1)! -1$

Published on 07 Sep 2016 - 19:00

score 6k · Answer 2 · 2026-04-10 17:02:20

6k

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Proof by induction on derivative

Published on 10 Apr 2026 - 17:02

score 103 · Answer 3 · 2016-09-08 19:07:01

103

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Prove by careful induction that if $r \in \mathbb{N}$, then $b^{2^r} - 1 = (b-1)(b+1)(b^2 + 1)(b^{2^{2}} + 1) ... (b^{2^{r-1}} + 1)$

Published on 08 Sep 2016 - 19:07

score 834 · Answer 4 · 2016-09-08 23:57:53

834

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Prove that $2^{n+1} \gt n^2$ for every positive integer $n$.

Published on 08 Sep 2016 - 23:57

score 1.2k · Answer 5 · 2026-04-12 15:32:45

1.2k

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Mistake in basic algebra, I think?

Published on 12 Apr 2026 - 15:32

score 644 · Answer 6 · 2026-04-12 22:25:06

644

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Proof using induction: $r!$ divides the product of $r$ consecutive integers

Published on 12 Apr 2026 - 22:25

score 708 · Answer 7 · 2016-09-09 22:18:57

708

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Prove 1 is the smallest natural number via induction.

Published on 09 Sep 2016 - 22:18

score 446 · Answer 8 · 2026-04-13 02:26:39

446

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Prove using induction $\ln(n!)\leqslant n\ln(n)$ for $n\geqslant 1$.

Published on 13 Apr 2026 - 2:26

score 240 · Answer 9 · 2026-04-13 00:32:16

240

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Prove that the expression is divisible by 247 for any natural number

Published on 13 Apr 2026 - 0:32

score 1.5k · Answer 10 · 2026-04-11 00:34:07

1.5k

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Solve Proof by Induction with 2 variables

Published on 11 Apr 2026 - 0:34

score 251 · Answer 11 · 2026-04-13 01:14:25

251

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Prove that this sequence, $a_n$ holds for every positive integer n by using induction.

Published on 13 Apr 2026 - 1:14

score 56 · Answer 12 · 2016-09-11 02:01:04

56

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Is this a valid proof for $n! \gt 2^n$ for $n \ge 4$

Published on 11 Sep 2016 - 2:01

score 91 · Answer 13 · 2016-09-11 17:29:45

91

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Induction proof $\sum_{k=1}^{n} k^{2} = \frac{1}{6} n(n+1)(2n+1)$

Published on 11 Sep 2016 - 17:29

score 1.1k · Answer 14 · 2026-04-11 02:24:46

1.1k

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Probability of heads using induction

Published on 11 Apr 2026 - 2:24

score 81 · Answer 15 · 2026-03-31 16:54:48

81

Views

Find the $\sup$ of the set.

Published on 31 Mar 2026 - 16:54

List Question

How would you prove that via induction? $\sum_{k=1}^{n}k! \cdot k= (n+1)! -1$

Proof by induction on derivative

Prove by careful induction that if $r \in \mathbb{N}$, then $b^{2^r} - 1 = (b-1)(b+1)(b^2 + 1)(b^{2^{2}} + 1) ... (b^{2^{r-1}} + 1)$

Prove that $2^{n+1} \gt n^2$ for every positive integer $n$.

Mistake in basic algebra, I think?

Proof using induction: $r!$ divides the product of $r$ consecutive integers

Prove 1 is the smallest natural number via induction.

Prove using induction $\ln(n!)\leqslant n\ln(n)$ for $n\geqslant 1$.

Prove that the expression is divisible by 247 for any natural number

Solve Proof by Induction with 2 variables

Prove that this sequence, $a_n$ holds for every positive integer n by using induction.

Is this a valid proof for $n! \gt 2^n$ for $n \ge 4$

Induction proof $\sum_{k=1}^{n} k^{2} = \frac{1}{6} n(n+1)(2n+1)$

Probability of heads using induction

Find the $\sup$ of the set.

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