Question

Strong Induction (verify solution of linear recurrence)

score 70 · Answer 1 · 2026-04-12 03:11:23

70

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Strong Induction (verify solution of linear recurrence)

Published on 12 Apr 2026 - 3:11

score 532 · Answer 2 · 2026-04-15 02:53:11

532

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Proving that $3 + 3 \times 5 + 3 \times 5^2 + \cdots+ 3 \times 5^n = [3(5^{n+1} - 1)] / 4$ whenever $n \geq 0$

Published on 15 Apr 2026 - 2:53

score 3.7k · Answer 3 · 2026-04-14 11:06:23

3.7k

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Using 4-cent and 11-cent stamps for postage (induction)

Published on 14 Apr 2026 - 11:06

score 1.1k · Answer 4 · 2026-04-16 13:25:42

1.1k

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Proving that $f_2+f_4+\cdots+f_{2n}=f_{2n+1}-1$ for Fibonacci numbers by induction

Published on 16 Apr 2026 - 13:25

score 696 · Answer 5 · 2026-04-09 15:09:08

696

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Need help with Knuth's proof for Gray Codes

Published on 09 Apr 2026 - 15:09

score 110 · Answer 6 · 2026-04-16 18:49:58

110

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Prove that $4 + 5 + 6 + \cdots+ n = \frac{n(n+1)}{3}$ for $n \ge 4$

Published on 16 Apr 2026 - 18:49

score 120 · Answer 7 · 2026-05-14 13:47:41

120

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Finding a closed form for $\sum^{n}_{k=1} \frac{k}{(k+1)!} $

Published on 14 May 2026 - 13:47

score 943 · Answer 8 · 2026-04-17 04:30:43

943

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Prove that $\Gamma(-k+\frac{1}{2})=\frac{(-1)^k 2^k}{1\cdot 3\cdot 5\cdots(2k-1)}\sqrt{\pi}$.

Published on 17 Apr 2026 - 4:30

score 291 · Answer 9 · 2026-04-12 04:14:46

291

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How is it that $(2^k+1)3 \gt (2^k+1)2\gt 2^{k+1}+2\gt 2^{k+1}+1$?

Published on 12 Apr 2026 - 4:14

score 116 · Answer 10 · 2026-04-14 00:22:19

116

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induction clarification about the step $n+1$

Published on 14 Apr 2026 - 0:22

score 61 · Answer 11 · 2026-04-11 17:33:27

61

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proof of an equivalence

Published on 11 Apr 2026 - 17:33

score 12.9k · Answer 12 · 2026-04-16 13:11:48

12.9k

Views

induction proof over graphs

Published on 16 Apr 2026 - 13:11

score 404 · Answer 13 · 2026-04-16 07:24:25

404

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Fibonacci Sequence: Prove $f_1+f_3+\dots+f_{2n-1}=f_{2n}$ by Induction.

Published on 16 Apr 2026 - 7:24

score 317 · Answer 14 · 2026-04-12 06:44:40

317

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Well-ordering principle and theorem

Published on 12 Apr 2026 - 6:44

score 183 · Answer 15 · 2026-04-16 16:51:43

183

Views

Inequality : $\sum_{k=1}^n x_k\cdot \sum_{k=1}^n \frac{1}{x_k} \geq n^2$

Published on 16 Apr 2026 - 16:51

List Question

Strong Induction (verify solution of linear recurrence)

Proving that $3 + 3 \times 5 + 3 \times 5^2 + \cdots+ 3 \times 5^n = [3(5^{n+1} - 1)] / 4$ whenever $n \geq 0$

Using 4-cent and 11-cent stamps for postage (induction)

Proving that $f_2+f_4+\cdots+f_{2n}=f_{2n+1}-1$ for Fibonacci numbers by induction

Need help with Knuth's proof for Gray Codes

Prove that $4 + 5 + 6 + \cdots+ n = \frac{n(n+1)}{3}$ for $n \ge 4$

Finding a closed form for $\sum^{n}_{k=1} \frac{k}{(k+1)!} $

Prove that $\Gamma(-k+\frac{1}{2})=\frac{(-1)^k 2^k}{1\cdot 3\cdot 5\cdots(2k-1)}\sqrt{\pi}$.

How is it that $(2^k+1)3 \gt (2^k+1)2\gt 2^{k+1}+2\gt 2^{k+1}+1$?

induction clarification about the step $n+1$

proof of an equivalence

induction proof over graphs

Fibonacci Sequence: Prove $f_1+f_3+\dots+f_{2n-1}=f_{2n}$ by Induction.

Well-ordering principle and theorem

Inequality : $\sum_{k=1}^n x_k\cdot \sum_{k=1}^n \frac{1}{x_k} \geq n^2$

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