Question

Proof by induction that $3^{n+1} > n^4$

score 95 · Answer 1 · 2026-04-14 14:29:16

95

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Proof by induction that $3^{n+1} > n^4$

Published on 14 Apr 2026 - 14:29

score 125 · Answer 2 · 2026-04-15 07:33:49

125

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Can I show $\frac{1}{n+1} + \frac{1}{n+2} + \cdots + \frac{1}{2n} \leq 1$ by induction?

Published on 15 Apr 2026 - 7:33

score 3.2k · Answer 3 · 2026-04-16 20:09:13

3.2k

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Graph Proof by induction.

Published on 16 Apr 2026 - 20:09

score 100 · Answer 4 · 2026-04-12 01:42:26

100

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proof by induction, the number of ways of grouping unlabelled objects

Published on 12 Apr 2026 - 1:42

score 4.8k · Answer 5 · 2026-04-15 20:35:49

4.8k

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Proving $(x+y)^n = \sum\limits_{k=0}^n \binom{n}{k} x^k y^{n-k}$

Published on 15 Apr 2026 - 20:35

score 46 · Answer 6 · 2026-04-11 15:20:18

46

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prove the inequality by induction for the folfowing expression

Published on 11 Apr 2026 - 15:20

score 187 · Answer 7 · 2026-04-10 19:50:46

187

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Proof of $n^{1/n} - 1 \le \sqrt{\frac 2n}$ by induction using binomial formula

Published on 10 Apr 2026 - 19:50

score 271 · Answer 8 · 2026-04-14 17:38:38

271

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Proving a log by induction

Published on 14 Apr 2026 - 17:38

score 2.7k · Answer 9 · 2026-04-11 04:14:03

2.7k

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Why induction can't work for infinite number?

Published on 11 Apr 2026 - 4:14

score 12.2k · Answer 10 · 2026-04-14 16:09:06

12.2k

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Induction proof: n lines in a plane

Published on 14 Apr 2026 - 16:09

score 122 · Answer 11 · 2026-04-12 05:29:23

122

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What's wrong with this (fake) proof that $ n=1\forall n\in \Bbb N$?

Published on 12 Apr 2026 - 5:29

score 3.3k · Answer 12 · 2026-04-16 11:58:29

3.3k

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Prove that a set having $n\geq 2$ elements has $\frac{n(n-1)}{2}$ subsets having exactly two elements.

Published on 16 Apr 2026 - 11:58

score 100 · Answer 13 · 2026-04-15 02:32:26

Find the smallest $N \in Z^+$ satisfying the property that $n^2 \leq 2^n$ for all $n \geq N$, and prove your result using induction.

score 174 · Answer 14 · 2026-04-12 13:05:02

174

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How can the proof by induction be reliable when it depends on the number of steps?

Published on 12 Apr 2026 - 13:05

score 1.6k · Answer 15 · 2026-04-14 12:21:10

1.6k

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Flaw in this proof by induction

Published on 14 Apr 2026 - 12:21

List Question

Proof by induction that $3^{n+1} > n^4$

Can I show $\frac{1}{n+1} + \frac{1}{n+2} + \cdots + \frac{1}{2n} \leq 1$ by induction?

Graph Proof by induction.

proof by induction, the number of ways of grouping unlabelled objects

Proving $(x+y)^n = \sum\limits_{k=0}^n \binom{n}{k} x^k y^{n-k}$

prove the inequality by induction for the folfowing expression

Proof of $n^{1/n} - 1 \le \sqrt{\frac 2n}$ by induction using binomial formula

Proving a log by induction

Why induction can't work for infinite number?

Induction proof: n lines in a plane

What's wrong with this (fake) proof that $ n=1\forall n\in \Bbb N$?

Prove that a set having $n\geq 2$ elements has $\frac{n(n-1)}{2}$ subsets having exactly two elements.

Find the smallest $N \in Z^+$ satisfying the property that $n^2 \leq 2^n$ for all $n \geq N$, and prove your result using induction.

How can the proof by induction be reliable when it depends on the number of steps?

Flaw in this proof by induction

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