Question

Prove by induction: $\sum_{k = 0}^n {{2n + 1}\choose{2k + 1}} = 4^n$

score 1.1k · Answer 1 · 2026-04-16 08:29:34

1.1k

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Prove by induction: $\sum_{k = 0}^n {{2n + 1}\choose{2k + 1}} = 4^n$

Published on 16 Apr 2026 - 8:29

score 76 · Answer 2 · 2026-04-13 19:08:50

76

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Prove matrix identity by induction

Published on 13 Apr 2026 - 19:08

score 410 · Answer 3 · 2026-04-16 03:31:52

410

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If $P_n$ is the statement $3^n>n,$ prove $P_{n+1}$ is true whenever $P_n$ is true.

Published on 16 Apr 2026 - 3:31

score 692 · Answer 4 · 2026-04-13 17:01:16

692

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Using mathematical induction prove that $ 11 \cdot 3^n + 3 \cdot 7^n - 6$ is divisible by 8

Published on 13 Apr 2026 - 17:01

score 53 · Answer 5 · 2026-04-17 08:41:43

53

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Induction for $1^2+3^2+5^2+...+(2n-1)^2= \binom{2n+1}{3}$

Published on 17 Apr 2026 - 8:41

score 386 · Answer 6 · 2026-04-11 19:02:51

386

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What's wrong with this induction proof?

Published on 11 Apr 2026 - 19:02

score 84 · Answer 7 · 2026-04-14 11:14:28

84

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Question on proof of $1+2+\dots+n=\frac{n(n+1)}{2}$ by induction.

Published on 14 Apr 2026 - 11:14

score 318 · Answer 8 · 2026-04-15 23:31:29

318

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Prove that $\ln{n} \lt \sqrt{n}$ for $n \in \mathbb{N}^{*}$ without derivative

Published on 15 Apr 2026 - 23:31

score 154 · Answer 9 · 2026-04-16 15:10:33

154

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Using induction to show that if $x_n^2 \geq 2$, then $x_{n+1}^2 \geq 2$

Published on 16 Apr 2026 - 15:10

score 61 · Answer 10 · 2026-04-15 02:13:39

61

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I have done this induction proof for the Fibonacci-sequence

Published on 15 Apr 2026 - 2:13

score 215 · Answer 11 · 2026-04-14 01:08:07

215

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Stuck in inductive step

Published on 14 Apr 2026 - 1:08

score 30 · Answer 12 · 2026-03-31 23:44:55

30

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extending finite properties

Published on 31 Mar 2026 - 23:44

score 526 · Answer 13 · 2026-04-16 10:43:37

526

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Any connected graph at most |V|+1 edges is 3-colourable

Published on 16 Apr 2026 - 10:43

score 349 · Answer 14 · 2026-04-09 02:07:19

349

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Does an induction argument work when $n \rightarrow \infty$?

Published on 09 Apr 2026 - 2:07

score 276 · Answer 15 · 2026-04-12 10:16:34

276

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How to do this induction proof?

Published on 12 Apr 2026 - 10:16

List Question

Prove by induction: $\sum_{k = 0}^n {{2n + 1}\choose{2k + 1}} = 4^n$

Prove matrix identity by induction

If $P_n$ is the statement $3^n>n,$ prove $P_{n+1}$ is true whenever $P_n$ is true.

Using mathematical induction prove that $ 11 \cdot 3^n + 3 \cdot 7^n - 6$ is divisible by 8

Induction for $1^2+3^2+5^2+...+(2n-1)^2= \binom{2n+1}{3}$

What's wrong with this induction proof?

Question on proof of $1+2+\dots+n=\frac{n(n+1)}{2}$ by induction.

Prove that $\ln{n} \lt \sqrt{n}$ for $n \in \mathbb{N}^{*}$ without derivative

Using induction to show that if $x_n^2 \geq 2$, then $x_{n+1}^2 \geq 2$

I have done this induction proof for the Fibonacci-sequence

Stuck in inductive step

extending finite properties

Any connected graph at most |V|+1 edges is 3-colourable

Does an induction argument work when $n \rightarrow \infty$?

How to do this induction proof?

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