Question

Proof of equality $\sum_{k=0}^{m}k^n = \sum_{k=0}^{n}k!{m+1\choose k+1} \left\{^n_k \right\} $ by induction

score 297 · Answer 1 · 2014-08-11 17:14:17

297

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Proof of equality $\sum_{k=0}^{m}k^n = \sum_{k=0}^{n}k!{m+1\choose k+1} \left\{^n_k \right\} $ by induction

Published on 11 Aug 2014 - 17:14

score 17.6k · Answer 2 · 2026-03-27 12:20:23

17.6k

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Proof by induction: $n$th Fibonacci number is at most $ 2^n$

Published on 27 Mar 2026 - 12:20

score 179 · Answer 3 · 2026-03-27 14:02:21

179

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using induction to prove that the formula for finding the n-th term of the Fibonacci sequence is:

Published on 27 Mar 2026 - 14:02

score 307 · Answer 4 · 2014-08-13 01:18:37

307

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How to simplify the formula for $n$th Fibonacci number when $n=2$?

Published on 13 Aug 2014 - 1:18

score 104 · Answer 5 · 2014-08-13 22:36:09

104

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Proof by Induction: $(1+x)^n \le 1+(2^n-1)x$

Published on 13 Aug 2014 - 22:36

score 13.2k · Answer 6 · 2014-08-14 01:40:58

13.2k

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Proving the geometric series $\sum_{i=0}^n r^i = \frac{1-r^{n+1}}{1-r}$ by induction for $n\geq 1$

Published on 14 Aug 2014 - 1:40

score 432 · Answer 7 · 2014-08-15 23:04:20

432

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Equivalence between "mathematical induction" and "transfinite induction" for natural numbers?

Published on 15 Aug 2014 - 23:04

score 190 · Answer 8 · 2026-03-26 12:50:36

190

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Flaw in proof that in a classroom with $n$ students, if there is a girl, then all students are girls

Published on 26 Mar 2026 - 12:50

score 157 · Answer 9 · 2026-03-26 12:42:33

157

Views

What's wrong with this induction based proof?

Published on 26 Mar 2026 - 12:42

score 708 · Answer 10 · 2026-03-26 03:10:48

708

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Induction proof for continued fractions

Published on 26 Mar 2026 - 3:10

score 135 · Answer 11 · 2026-04-02 13:01:18

135

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Readings on more general/abstract notions of induction related to logic

Published on 02 Apr 2026 - 13:01

score 485 · Answer 12 · 2026-03-27 11:49:05

485

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Different proofs of $\,a^n-b^n =(a-b)\sum_{i=0}^{n-1} a^i b^{n-1-i} $?

Published on 27 Mar 2026 - 11:49

score 243 · Answer 13 · 2014-08-18 11:10:44

243

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Proof of equation $\sum_{k}{n\brack k}a_k = n!2^{n-1}$ by induction

Published on 18 Aug 2014 - 11:10

score 49 · Answer 14 · 2014-08-18 17:03:54

49

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how to prove using induction that sum of terms?

Published on 18 Aug 2014 - 17:03

score 110 · Answer 15 · 2014-08-18 17:11:45

110

Views

Show that $(n+1)^{n+1}>(n+2)^n$ for all positive integers

Published on 18 Aug 2014 - 17:11

List Question

Proof of equality $\sum_{k=0}^{m}k^n = \sum_{k=0}^{n}k!{m+1\choose k+1} \left\{^n_k \right\} $ by induction

Proof by induction: $n$th Fibonacci number is at most $ 2^n$

using induction to prove that the formula for finding the n-th term of the Fibonacci sequence is:

How to simplify the formula for $n$th Fibonacci number when $n=2$?

Proof by Induction: $(1+x)^n \le 1+(2^n-1)x$

Proving the geometric series $\sum_{i=0}^n r^i = \frac{1-r^{n+1}}{1-r}$ by induction for $n\geq 1$

Equivalence between "mathematical induction" and "transfinite induction" for natural numbers?

Flaw in proof that in a classroom with $n$ students, if there is a girl, then all students are girls

What's wrong with this induction based proof?

Induction proof for continued fractions

Readings on more general/abstract notions of induction related to logic

Different proofs of $\,a^n-b^n =(a-b)\sum_{i=0}^{n-1} a^i b^{n-1-i} $?

Proof of equation $\sum_{k}{n\brack k}a_k = n!2^{n-1}$ by induction

how to prove using induction that sum of terms?

Show that $(n+1)^{n+1}>(n+2)^n$ for all positive integers

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