Question

Prove using induction that $1^2 + 3^2 + 5^2 + . . . + (2n + 1)^2 = (n + 1) ∗ (2n + 1) ∗ (2n + 3)/3$

score 71 · Answer 1 · 2026-04-05 23:19:38

71

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Prove using induction that $1^2 + 3^2 + 5^2 + . . . + (2n + 1)^2 = (n + 1) ∗ (2n + 1) ∗ (2n + 3)/3$

Published on 05 Apr 2026 - 23:19

score 1.5k · Answer 2 · 2026-04-05 23:28:29

1.5k

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Prove that any integer amount of postage from 18 cents and up can be made using only 4-cent and 7-cent stamp. Assume an infinite supply of stamps

Published on 05 Apr 2026 - 23:28

score 2k · Answer 3 · 2020-03-10 23:19:45

2k

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Proving that every natural number can be written as a product of odd integer and a a non-negative integer power of 2.

Published on 10 Mar 2020 - 23:19

score 607 · Answer 4 · 2026-03-26 09:39:16

607

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Induction on grid Hamiltonian graph

Published on 26 Mar 2026 - 9:39

score 58 · Answer 5 · 2020-03-11 15:01:43

58

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Inductive hypothesis of constructive induction

Published on 11 Mar 2020 - 15:01

score 105 · Answer 6 · 2020-03-11 17:53:41

105

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Prove that the sequence $ x_{n+2}=\frac{4x_{n+1}^{3}-x_{n+1}^{2}x_{n}}{x_{n+1}x_{n} +x_{n}^{2}} $ is increasing

Published on 11 Mar 2020 - 17:53

score 28 · Answer 7 · 2026-04-08 16:22:14

28

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Proof by induction on First Order Formula

Published on 08 Apr 2026 - 16:22

score 370 · Answer 8 · 2020-03-11 21:24:35

370

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Let X and Y be nonempty finite sets and let F be the set of functions from X to Y. Prove that $|F| = |Y|^{|X|}$

Published on 11 Mar 2020 - 21:24

score 62 · Answer 9 · 2020-03-12 02:11:25

62

Views

Show by Induction, but stuck on Induction Step (Don't know how to implement N = K+1)

Published on 12 Mar 2020 - 2:11

score 129 · Answer 10 · 2020-03-12 20:06:28

129

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The meaning of $\ast$ in $\{0,1\}^\ast$ and of $\lambda$ such that $\forall x\in\{0,1\}^\ast$ we have $\lambda x=x$.

Published on 12 Mar 2020 - 20:06

score 247 · Answer 11 · 2026-04-09 01:07:10

247

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Proof of induction of the area formula of a rectangle when its two sides are natural numbers

Published on 09 Apr 2026 - 1:07

score 317 · Answer 12 · 2026-03-27 23:15:44

317

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Proof that $C(n , 0) + C(n+1 , 1) + C(n+2 , 2) + ... + C(n + k , k) =C(n+k+1 , k)$

Published on 27 Mar 2026 - 23:15

score 110 · Answer 13 · 2020-03-13 17:54:38

110

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Prove $p_1 \iff p_2 \iff p_3 \iff \ldots \iff p_n$ by using Proof by Induction.

Published on 13 Mar 2020 - 17:54

score 117 · Answer 14 · 2026-04-08 17:28:03

117

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Proof by induction of inadequacy of a propositional connective

Published on 08 Apr 2026 - 17:28

score 37 · Answer 15 · 2020-03-14 12:46:35

37

Views

Prove that $\sum \leq \frac{3n-2}{2n-1}$

Published on 14 Mar 2020 - 12:46

List Question

Prove using induction that $1^2 + 3^2 + 5^2 + . . . + (2n + 1)^2 = (n + 1) ∗ (2n + 1) ∗ (2n + 3)/3$

Prove that any integer amount of postage from 18 cents and up can be made using only 4-cent and 7-cent stamp. Assume an infinite supply of stamps

Proving that every natural number can be written as a product of odd integer and a a non-negative integer power of 2.

Induction on grid Hamiltonian graph

Inductive hypothesis of constructive induction

Prove that the sequence $ x_{n+2}=\frac{4x_{n+1}^{3}-x_{n+1}^{2}x_{n}}{x_{n+1}x_{n} +x_{n}^{2}} $ is increasing

Proof by induction on First Order Formula

Let X and Y be nonempty finite sets and let F be the set of functions from X to Y. Prove that $|F| = |Y|^{|X|}$

Show by Induction, but stuck on Induction Step (Don't know how to implement N = K+1)

The meaning of $\ast$ in $\{0,1\}^\ast$ and of $\lambda$ such that $\forall x\in\{0,1\}^\ast$ we have $\lambda x=x$.

Proof of induction of the area formula of a rectangle when its two sides are natural numbers

Proof that $C(n , 0) + C(n+1 , 1) + C(n+2 , 2) + ... + C(n + k , k) =C(n+k+1 , k)$

Prove $p_1 \iff p_2 \iff p_3 \iff \ldots \iff p_n$ by using Proof by Induction.

Proof by induction of inadequacy of a propositional connective

Prove that $\sum \leq \frac{3n-2}{2n-1}$

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