Question

Prove by induction $(n+1) + (n + 2) +\dots + (2n - 1 ) + (2n) = \frac{n(3n + 1)}{2}$, $n \geq 1$

score 68 · Answer 1 · 2026-03-25 22:05:36

68

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Prove by induction $(n+1) + (n + 2) +\dots + (2n - 1 ) + (2n) = \frac{n(3n + 1)}{2}$, $n \geq 1$

Published on 25 Mar 2026 - 22:05

score 149 · Answer 2 · 2019-01-17 18:54:30

149

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Taking a hypothesis and using a list of tautologies to prove a conclusion

Published on 17 Jan 2019 - 18:54

score 71 · Answer 3 · 2019-01-18 18:35:51

71

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Induction of $\sum^n_{k=2} 1 - 1/k^2 =(1+n)/(2n)$

Published on 18 Jan 2019 - 18:35

score 43 · Answer 4 · 2019-01-19 12:12:39

43

Views

Proof question that could be proved using mathematical induction.

Published on 19 Jan 2019 - 12:12

score 81 · Answer 5 · 2026-03-25 23:36:10

81

Views

Using Induction to prove a product series equality?

Published on 25 Mar 2026 - 23:36

score 341 · Answer 6 · 2026-03-29 10:07:52

341

Views

Prove $\sum 3^k = O(3^n)$

Published on 29 Mar 2026 - 10:07

score 31 · Answer 7 · 2026-03-26 03:19:14

31

Views

Using Induction to prove this inequality?

Published on 26 Mar 2026 - 3:19

score 224 · Answer 8 · 2019-01-20 20:04:58

224

Views

Prove by induction: For $n\in{\Bbb N}$ and $n\geq{12}$ there are $a,b\in\Bbb{N}$ such that: $n=4a+5b$.

Published on 20 Jan 2019 - 20:04

score 125 · Answer 9 · 2019-01-20 23:59:44

125

Views

Proving $\binom{n + m}{r} = \sum_{i = 0}^{r} \binom{n}{i}\binom{m}{r - i}$

Published on 20 Jan 2019 - 23:59

score 54 · Answer 10 · 2019-01-21 02:41:00

54

Views

Confused about a mathematical induction detail

Published on 21 Jan 2019 - 2:41

score 97 · Answer 11 · 2026-03-25 23:42:19

97

Views

Show that if $2^k\in S\space\space\forall k\in\mathbb{N}$, and if $k\in S$ and $k\ge2$, then $k-1\in S$, then $S=\mathbb{N}$

Published on 25 Mar 2026 - 23:42

score 115 · Answer 12 · 2026-03-26 08:02:19

115

Views

Let $(F_n)_{n\in \mathbb{N}}$ be the Fibonacci sequence. Prove that $F_{n+1}F_n - F_{n-1}F_{n-2} = F_{2n-1}$.

Published on 26 Mar 2026 - 8:02

score 3.1k · Answer 13 · 2019-01-23 19:26:05

3.1k

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Prove that $n! > n^{3}$ for every integer $n \ge 6$ using induction

Published on 23 Jan 2019 - 19:26

score 56 · Answer 14 · 2019-01-24 07:55:05

56

Views

Use the principle of mathematical induction to prove [(1/2)+(1/2)+(1/3)+. . . (1/n)] ≤ (n/2)+1 for all n ϵ z+

Published on 24 Jan 2019 - 7:55

score 157 · Answer 15 · 2019-01-24 10:25:30

157

Views

Is my proof of $x^n-y^n = \ldots$ correct?

Published on 24 Jan 2019 - 10:25

List Question

Prove by induction $(n+1) + (n + 2) +\dots + (2n - 1 ) + (2n) = \frac{n(3n + 1)}{2}$, $n \geq 1$

Taking a hypothesis and using a list of tautologies to prove a conclusion

Induction of $\sum^n_{k=2} 1 - 1/k^2 =(1+n)/(2n)$

Proof question that could be proved using mathematical induction.

Using Induction to prove a product series equality?

Prove $\sum 3^k = O(3^n)$

Using Induction to prove this inequality?

Prove by induction: For $n\in{\Bbb N}$ and $n\geq{12}$ there are $a,b\in\Bbb{N}$ such that: $n=4a+5b$.

Proving $\binom{n + m}{r} = \sum_{i = 0}^{r} \binom{n}{i}\binom{m}{r - i}$

Confused about a mathematical induction detail

Show that if $2^k\in S\space\space\forall k\in\mathbb{N}$, and if $k\in S$ and $k\ge2$, then $k-1\in S$, then $S=\mathbb{N}$

Let $(F_n)_{n\in \mathbb{N}}$ be the Fibonacci sequence. Prove that $F_{n+1}F_n - F_{n-1}F_{n-2} = F_{2n-1}$.

Prove that $n! > n^{3}$ for every integer $n \ge 6$ using induction

Use the principle of mathematical induction to prove [(1/2)+(1/2)+(1/3)+. . . (1/n)] ≤ (n/2)+1 for all n ϵ z+

Is my proof of $x^n-y^n = \ldots$ correct?

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