Question

Prove $n^3 + 7n + 3$ is divisible by 3 for all integers n ≥ 0

score 4.4k · Answer 1 · 2026-04-14 20:16:28

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Prove $n^3 + 7n + 3$ is divisible by 3 for all integers n ≥ 0

Published on 14 Apr 2026 - 20:16

score 131 · Answer 2 · 2026-04-15 18:51:11

131

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Proof by induction: $(a+b)^n=a^n+na^{n-1}b+\frac{n(n-1)}{2!}a^{n-2}b^2+...+nab^{n-1}+b^n$

Published on 15 Apr 2026 - 18:51

score 65 · Answer 3 · 2026-04-04 13:44:00

65

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Require assistance proving $n≥2 \Longrightarrow \frac{n!}{n^n} ≤ \frac{1}{2}^{\lfloor \frac{n}{2}\rfloor}$

Published on 04 Apr 2026 - 13:44

score 125 · Answer 4 · 2026-04-16 11:05:07

125

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Finding an expression for the sum of n tems of the series $1^2 + 2^2 + 3^2 + ... + n^2$

Published on 16 Apr 2026 - 11:05

score 2.3k · Answer 5 · 2026-04-15 20:15:23

2.3k

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Any collection of n coins can be obtained using a combination of 3¢ and 5¢ coins where n ≥ 14

Published on 15 Apr 2026 - 20:15

score 91 · Answer 6 · 2026-04-14 20:11:38

91

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Proof that $\lfloor x + x\sqrt3 \rfloor = x + \lfloor x\sqrt3 \rfloor$ Where $x \in N$

Published on 14 Apr 2026 - 20:11

score 94 · Answer 7 · 2026-04-16 15:14:24

94

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Proving $\frac{n}{n+1} < \frac{n+1}{n+2}$ by induction?

Published on 16 Apr 2026 - 15:14

score 455 · Answer 8 · 2026-04-09 21:05:55

455

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Differentiate a geometric sum and show that it is less than an equation

Published on 09 Apr 2026 - 21:05

score 2.2k · Answer 9 · 2026-04-09 17:06:24

2.2k

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What do we actually prove using induction theorem?

Published on 09 Apr 2026 - 17:06

score 55 · Answer 10 · 2026-04-14 03:53:56

55

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Prove that $\frac{(a+1)^k}{a^k+1} \leq 2^{k-1}$

Published on 14 Apr 2026 - 3:53

score 47 · Answer 11 · 2026-04-09 16:58:02

47

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Is my proof by induction correct?

Published on 09 Apr 2026 - 16:58

score 146 · Answer 12 · 2026-04-13 04:51:18

146

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Structural induction proof

Published on 13 Apr 2026 - 4:51

score 266 · Answer 13 · 2026-04-14 00:58:57

266

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How many maps can exist between two sets?

Published on 14 Apr 2026 - 0:58

score 128 · Answer 14 · 2026-04-16 19:15:08

128

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$\frac{1\cdot2^2+2\cdot3^2+\cdots+n(n+1)^2}{1^2\cdot2+2^2\cdot3+\cdots+n^2(n+1)}=\frac{3n+5}{3n+1}$ by Mathematical Induction

Published on 16 Apr 2026 - 19:15

score 2.5k · Answer 15 · 2026-04-16 07:21:51

2.5k

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Probability of an even number of sixes

Published on 16 Apr 2026 - 7:21

List Question

Prove $n^3 + 7n + 3$ is divisible by 3 for all integers n ≥ 0

Proof by induction: $(a+b)^n=a^n+na^{n-1}b+\frac{n(n-1)}{2!}a^{n-2}b^2+...+nab^{n-1}+b^n$

Require assistance proving $n≥2 \Longrightarrow \frac{n!}{n^n} ≤ \frac{1}{2}^{\lfloor \frac{n}{2}\rfloor}$

Finding an expression for the sum of n tems of the series $1^2 + 2^2 + 3^2 + ... + n^2$

Any collection of n coins can be obtained using a combination of 3¢ and 5¢ coins where n ≥ 14

Proof that $\lfloor x + x\sqrt3 \rfloor = x + \lfloor x\sqrt3 \rfloor$ Where $x \in N$

Proving $\frac{n}{n+1} < \frac{n+1}{n+2}$ by induction?

Differentiate a geometric sum and show that it is less than an equation

What do we actually prove using induction theorem?

Prove that $\frac{(a+1)^k}{a^k+1} \leq 2^{k-1}$

Is my proof by induction correct?

Structural induction proof

How many maps can exist between two sets?

$\frac{1\cdot2^2+2\cdot3^2+\cdots+n(n+1)^2}{1^2\cdot2+2^2\cdot3+\cdots+n^2(n+1)}=\frac{3n+5}{3n+1}$ by Mathematical Induction

Probability of an even number of sixes

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