Question

Prove By Mathematical Induction That $\forall n\in \Bbb N,~\frac{n(n+1)(n+2)}{6}\in \Bbb N$

score 107 · Answer 1 · 2026-04-15 19:49:21

107

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Prove By Mathematical Induction That $\forall n\in \Bbb N,~\frac{n(n+1)(n+2)}{6}\in \Bbb N$

Published on 15 Apr 2026 - 19:49

score 293 · Answer 2 · 2026-04-13 19:53:19

293

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Spreading news: Prove $2n-4$ by induction.

Published on 13 Apr 2026 - 19:53

score 96 · Answer 3 · 2026-04-16 04:44:41

96

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Prove that the ant can survive

Published on 16 Apr 2026 - 4:44

score 622 · Answer 4 · 2026-04-17 09:45:33

622

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Prove by induction that $1+3+3^2+3^3+...+3^n=\frac{1}{2}(3^{n+1}-1)$

Published on 17 Apr 2026 - 9:45

score 50 · Answer 5 · 2026-04-09 14:43:23

50

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How do I express a series where the first term is positive and all subsequent terms are negative?

Published on 09 Apr 2026 - 14:43

score 48 · Answer 6 · 2026-04-16 04:23:15

48

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Permuting k elements out of n

Published on 16 Apr 2026 - 4:23

score 267 · Answer 7 · 2026-04-16 07:27:36

267

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Prove by induction: $\sin{x}+\sin{3x}+\dots+\sin{(2n-1)x}=\frac{\sin^2{nx}}{\sin{x}}$

Published on 16 Apr 2026 - 7:27

score 79 · Answer 8 · 2026-04-17 21:26:36

79

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Showing $3^n=\sum_{k=0}^n{(-1)^k\binom{n}{k}4^{n-k}}$.

Published on 17 Apr 2026 - 21:26

score 61 · Answer 9 · 2026-04-16 09:57:17

61

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Prove $\frac12+\frac16+...+\frac{1}{n(n+1)}=\frac{n}{n+1}$ for $n \in \mathbb{N}$

Published on 16 Apr 2026 - 9:57

score 134 · Answer 10 · 2026-04-15 01:43:08

134

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Prove that $(\sum_{i=1}^n i)^2$ = $\sum_{i=1}^n i^3$ by induction

Published on 15 Apr 2026 - 1:43

score 929 · Answer 11 · 2026-04-16 09:55:45

929

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If m,n,p,q are non negative integers, then how to prove the following?

Published on 16 Apr 2026 - 9:55

score 54 · Answer 12 · 2026-04-10 18:34:56

54

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Mathematical Induction and Powers

Published on 10 Apr 2026 - 18:34

score 40 · Answer 13 · 2026-04-09 00:11:48

40

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Proof by Induction: Help?

Published on 09 Apr 2026 - 0:11

score 109 · Answer 14 · 2026-04-15 20:00:05

109

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Prove that $n \geq \sqrt{n-1} + \sqrt{n}$ for $n \geq 4$

Published on 15 Apr 2026 - 20:00

score 196 · Answer 15 · 2026-04-13 19:24:10

196

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Combinatorial determinant & Vandermonde relation

Published on 13 Apr 2026 - 19:24

List Question

Prove By Mathematical Induction That $\forall n\in \Bbb N,~\frac{n(n+1)(n+2)}{6}\in \Bbb N$

Spreading news: Prove $2n-4$ by induction.

Prove that the ant can survive

Prove by induction that $1+3+3^2+3^3+...+3^n=\frac{1}{2}(3^{n+1}-1)$

How do I express a series where the first term is positive and all subsequent terms are negative?

Permuting k elements out of n

Prove by induction: $\sin{x}+\sin{3x}+\dots+\sin{(2n-1)x}=\frac{\sin^2{nx}}{\sin{x}}$

Showing $3^n=\sum_{k=0}^n{(-1)^k\binom{n}{k}4^{n-k}}$.

Prove $\frac12+\frac16+...+\frac{1}{n(n+1)}=\frac{n}{n+1}$ for $n \in \mathbb{N}$

Prove that $(\sum_{i=1}^n i)^2$ = $\sum_{i=1}^n i^3$ by induction

If m,n,p,q are non negative integers, then how to prove the following?

Mathematical Induction and Powers

Proof by Induction: Help?

Prove that $n \geq \sqrt{n-1} + \sqrt{n}$ for $n \geq 4$

Combinatorial determinant & Vandermonde relation

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