Question

Induction proof concerning Pell numbers

score 982 · Answer 1 · 2026-04-25 19:44:14

982

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Induction proof concerning Pell numbers

Published on 25 Apr 2026 - 19:44

score 457 · Answer 2 · 2026-04-19 05:04:33

457

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Use induction to prove that sum of the first $2n$ terms of the series $1^2-3^2+5^2-7^2+…$ is $-8n^2$.

Published on 19 Apr 2026 - 5:04

score 71 · Answer 3 · 2026-04-14 07:01:05

71

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Show if $0 \le a <b$ implies $0 \le a^{\frac{1}{n}}<b^{\frac{1}{n}}$

Published on 14 Apr 2026 - 7:01

score 190 · Answer 4 · 2026-04-15 20:35:40

190

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Proving with induction $(1-x)^n<\frac 1 {1+nx}$

Published on 15 Apr 2026 - 20:35

score 127 · Answer 5 · 2026-04-16 18:15:18

127

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Using induction to show associativity on $x_1+\dots + x_n$

Published on 16 Apr 2026 - 18:15

score 281 · Answer 6 · 2026-04-11 14:25:42

281

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Proof of Binomial Formula Summation - Induction

Published on 11 Apr 2026 - 14:25

score 42 · Answer 7 · 2026-04-16 09:09:22

42

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Use induction to show $a_n$ is no greater than $4\log_2(\log_2(n))$

Published on 16 Apr 2026 - 9:09

score 4.9k · Answer 8 · 2026-04-15 22:48:40

4.9k

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Proving that two summations are equivalent: $\sum_{i=1}^n i^3 = (\sum_{i=1}^n i)^2$

Published on 15 Apr 2026 - 22:48

score 644 · Answer 9 · 2026-04-12 03:13:41

644

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Inductive step in proof of Freshman's Dream

Published on 12 Apr 2026 - 3:13

score 96 · Answer 10 · 2026-04-14 03:44:44

96

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Proving with a given definition that if $|A|=|B|$ then $A,B$ are equivalent (with induction but without using the induction hypothesis)

Published on 14 Apr 2026 - 3:44

score 78 · Answer 11 · 2026-04-17 13:46:47

78

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Prove this inequality.

Published on 17 Apr 2026 - 13:46

score 870 · Answer 12 · 2026-04-11 09:17:42

870

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Proving a Statement using Mathematical Induction

Published on 11 Apr 2026 - 9:17

score 126 · Answer 13 · 2026-04-13 07:40:57

126

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Demonstration of sum of powers of $2$

Published on 13 Apr 2026 - 7:40

score 640 · Answer 14 · 2026-04-17 04:29:53

640

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Prove that a recurrence relation (containing two recurrences) equals a given closed-form formula.

Published on 17 Apr 2026 - 4:29

score 216 · Answer 15 · 2026-04-12 20:49:33

216

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Does Induction theorem fails here at Euler's conjecture?

Published on 12 Apr 2026 - 20:49

List Question

Induction proof concerning Pell numbers

Use induction to prove that sum of the first $2n$ terms of the series $1^2-3^2+5^2-7^2+…$ is $-8n^2$.

Show if $0 \le a <b$ implies $0 \le a^{\frac{1}{n}}<b^{\frac{1}{n}}$

Proving with induction $(1-x)^n<\frac 1 {1+nx}$

Using induction to show associativity on $x_1+\dots + x_n$

Proof of Binomial Formula Summation - Induction

Use induction to show $a_n$ is no greater than $4\log_2(\log_2(n))$

Proving that two summations are equivalent: $\sum_{i=1}^n i^3 = (\sum_{i=1}^n i)^2$

Inductive step in proof of Freshman's Dream

Proving with a given definition that if $|A|=|B|$ then $A,B$ are equivalent (with induction but without using the induction hypothesis)

Prove this inequality.

Proving a Statement using Mathematical Induction

Demonstration of sum of powers of $2$

Prove that a recurrence relation (containing two recurrences) equals a given closed-form formula.

Does Induction theorem fails here at Euler's conjecture?

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