Question

Prove using induction that $2^n < \binom{2n}{n} < 4^n$ for $n \geq 2$

score 130 · Answer 1 · 2026-04-15 12:39:27

130

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Prove using induction that $2^n < \binom{2n}{n} < 4^n$ for $n \geq 2$

Published on 15 Apr 2026 - 12:39

score 86 · Answer 2 · 2026-04-13 20:59:33

86

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Proof by induction that $3\mid n^3-n$ - confused about inductive step

Published on 13 Apr 2026 - 20:59

score 19.5k · Answer 3 · 2026-04-15 11:35:30

19.5k

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Prove $\sum^n_{i=1} (2i-1)=n^2$ by induction

Published on 15 Apr 2026 - 11:35

score 231 · Answer 4 · 2026-04-12 04:23:37

231

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Difference between Inductive hypothesis and inductive goal

Published on 12 Apr 2026 - 4:23

score 4.3k · Answer 5 · 2026-04-16 11:05:18

4.3k

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Use mathematical induction to show that $ H_{2^n} \geq 1+ \frac{n}{2} $

Published on 16 Apr 2026 - 11:05

score 510 · Answer 6 · 2026-04-10 09:47:58

510

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Clarification on tribonacci numbers exercise

Published on 10 Apr 2026 - 9:47

score 41 · Answer 7 · 2026-04-14 22:42:38

Proof that for $a>0$ and $a + 1/a$ element of $\mathbb{Z}$, $a^n + 1/a^n$ is always element of $\mathbb{Z}$ by induction

score 798 · Answer 8 · 2026-04-16 11:02:29

798

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Proving a Fibonacci identity: $F_{2n} = F_n (F_{n+1} + F_{n-1})$

Published on 16 Apr 2026 - 11:02

score 78 · Answer 9 · 2026-04-15 08:26:08

78

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Inductive step for the Fibonacci sequence

Published on 15 Apr 2026 - 8:26

score 56 · Answer 10 · 2026-03-29 12:38:47

56

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Can someone explain the cancellation in this Induction proof? (Harmonic Sequence)

Published on 29 Mar 2026 - 12:38

score 3.6k · Answer 11 · 2015-10-30 22:15:39

3.6k

Views

Writing proofs with modular arithmetic

Published on 30 Oct 2015 - 22:15

score 95 · Answer 12 · 2026-04-13 19:54:38

95

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For which $n ≥ 0$ is $2^n + 2 · 3^n$ divisible by $8$?

Published on 13 Apr 2026 - 19:54

score 269 · Answer 13 · 2026-04-13 20:03:46

269

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Proof by induction for tricky double summation: $(\sum_{k=1}^n x_k)\cdot(\sum_{k=1}^n \frac{1}{x_k})\ge{n^2}$

Published on 13 Apr 2026 - 20:03

score 68 · Answer 14 · 2026-04-11 17:04:27

68

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Inductive proof showing that nilpotency is preserved by product, question on exact hypothesis

Published on 11 Apr 2026 - 17:04

score 445 · Answer 15 · 2026-04-09 08:36:23

445

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Is Minimal counterexample proof just induction in disguise?

Published on 09 Apr 2026 - 8:36

List Question

Prove using induction that $2^n < \binom{2n}{n} < 4^n$ for $n \geq 2$

Proof by induction that $3\mid n^3-n$ - confused about inductive step

Prove $\sum^n_{i=1} (2i-1)=n^2$ by induction

Difference between Inductive hypothesis and inductive goal

Use mathematical induction to show that $ H_{2^n} \geq 1+ \frac{n}{2} $

Clarification on tribonacci numbers exercise

Proof that for $a>0$ and $a + 1/a$ element of $\mathbb{Z}$, $a^n + 1/a^n$ is always element of $\mathbb{Z}$ by induction

Proving a Fibonacci identity: $F_{2n} = F_n (F_{n+1} + F_{n-1})$

Inductive step for the Fibonacci sequence

Can someone explain the cancellation in this Induction proof? (Harmonic Sequence)

Writing proofs with modular arithmetic

For which $n ≥ 0$ is $2^n + 2 · 3^n$ divisible by $8$?

Proof by induction for tricky double summation: $(\sum_{k=1}^n x_k)\cdot(\sum_{k=1}^n \frac{1}{x_k})\ge{n^2}$

Inductive proof showing that nilpotency is preserved by product, question on exact hypothesis

Is Minimal counterexample proof just induction in disguise?

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