Question

Prove by induction: A tree on $n\ge 2$ vertices has at least 2 leaves

score 9k · Answer 1 · 2026-03-31 23:08:15

9k

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Prove by induction: A tree on $n\ge 2$ vertices has at least 2 leaves

Published on 31 Mar 2026 - 23:08

score 600 · Answer 2 · 2026-04-15 21:44:15

600

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Establish by mathematical induction that a set having $n$ elements has $2^n$ subsets.

Published on 15 Apr 2026 - 21:44

score 346 · Answer 3 · 2026-04-15 08:36:04

346

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Prove that any postage greater than 17 can be made using 4 and 7 cent stamps

Published on 15 Apr 2026 - 8:36

score 1.1k · Answer 4 · 2026-04-11 19:15:14

1.1k

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Proving a $\cos(2nx)$ identity using induction

Published on 11 Apr 2026 - 19:15

score 154 · Answer 5 · 2026-04-11 01:21:08

154

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An induction problem that I can't think of an approach.

Published on 11 Apr 2026 - 1:21

score 66 · Answer 6 · 2026-04-17 11:53:06

66

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Prove by induction that $\sum_{k=1}^nk^p < (n+1)^{p+1}/(p+1), \quad n,p \in \mathbb{N}$

Published on 17 Apr 2026 - 11:53

score 57 · Answer 7 · 2026-03-26 19:02:48

57

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Induction to prove that for any $r \in \mathbb{R}$ such tht $r \notin (0,1)$ $\sum_{i=1}^n r^i-1 = \frac{(1-r^n)}{1-r}$ for all $n \in \mathbb{N}$.

Published on 26 Mar 2026 - 19:02

score 117 · Answer 8 · 2026-04-14 07:54:46

117

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Prove that $\sum_{k=1}^n \frac{1}{n+k} = \sum_{k=1}^{2n} \frac{1}{k}(-1)^{k-1}$ using induction

Published on 14 Apr 2026 - 7:54

score 71 · Answer 9 · 2026-04-14 22:07:47

71

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Use the rule for differentiating a product to prove that the derivative of $x^n$ is $nx^{n-1}$ for all $n∈N$.

Published on 14 Apr 2026 - 22:07

score 4.5k · Answer 10 · 2026-04-15 21:13:19

4.5k

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Use induction to prove that $2^n \gt n^3$ for every integer $n \ge 10$.

Published on 15 Apr 2026 - 21:13

score 49 · Answer 11 · 2026-04-16 03:41:15

49

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Prove that if $n \in \mathbb{N}$ and $n \ge 2$, then $2^{n + 1} \le 3^n$.

Published on 16 Apr 2026 - 3:41

score 335 · Answer 12 · 2026-04-16 15:58:10

335

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Prove inequality $\frac{a_1a_2...a_n}{(a_1+a_2+...+a_n)^n}\le \frac{(1-a_1)(1-a_2)...(1-a_n)}{(n-a_1-a_2-...-a_n)^n}$

Published on 16 Apr 2026 - 15:58

score 1.1k · Answer 13 · 2026-03-27 14:59:12

1.1k

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Prove that L is a sub-language of the CFG G by using induction. (CFG,Induction,School)

Published on 27 Mar 2026 - 14:59

score 97 · Answer 14 · 2026-04-16 07:28:14

97

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An inequality $\frac1{(n+1)^{1/(n+1)}}-\frac1{n^{1/n}}\le \frac1{n+1}$

Published on 16 Apr 2026 - 7:28

score 1.2k · Answer 15 · 2026-04-15 08:25:56

1.2k

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Induction Proof $2 + 5 + 8 + 11 + \cdots + (9n - 1) = \frac{3n(9n + 1)}{ 2}$

Published on 15 Apr 2026 - 8:25

List Question

Prove by induction: A tree on $n\ge 2$ vertices has at least 2 leaves

Establish by mathematical induction that a set having $n$ elements has $2^n$ subsets.

Prove that any postage greater than 17 can be made using 4 and 7 cent stamps

Proving a $\cos(2nx)$ identity using induction

An induction problem that I can't think of an approach.

Prove by induction that $\sum_{k=1}^nk^p < (n+1)^{p+1}/(p+1), \quad n,p \in \mathbb{N}$

Induction to prove that for any $r \in \mathbb{R}$ such tht $r \notin (0,1)$ $\sum_{i=1}^n r^i-1 = \frac{(1-r^n)}{1-r}$ for all $n \in \mathbb{N}$.

Prove that $\sum_{k=1}^n \frac{1}{n+k} = \sum_{k=1}^{2n} \frac{1}{k}(-1)^{k-1}$ using induction

Use the rule for differentiating a product to prove that the derivative of $x^n$ is $nx^{n-1}$ for all $n∈N$.

Use induction to prove that $2^n \gt n^3$ for every integer $n \ge 10$.

Prove that if $n \in \mathbb{N}$ and $n \ge 2$, then $2^{n + 1} \le 3^n$.

Prove inequality $\frac{a_1a_2...a_n}{(a_1+a_2+...+a_n)^n}\le \frac{(1-a_1)(1-a_2)...(1-a_n)}{(n-a_1-a_2-...-a_n)^n}$

Prove that L is a sub-language of the CFG G by using induction. (CFG,Induction,School)

An inequality $\frac1{(n+1)^{1/(n+1)}}-\frac1{n^{1/n}}\le \frac1{n+1}$

Induction Proof $2 + 5 + 8 + 11 + \cdots + (9n - 1) = \frac{3n(9n + 1)}{ 2}$

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