Question

Expanding a Proof of Induction on $\Bbb N $ to $\Bbb Q $ (Linear Algebra)

score 71 · Answer 1 · 2026-04-13 08:04:57

71

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Expanding a Proof of Induction on $\Bbb N $ to $\Bbb Q $ (Linear Algebra)

Published on 13 Apr 2026 - 8:04

score 232 · Answer 2 · 2026-04-12 21:24:40

232

Views

Prove that the identity is true for all natural numbers

Published on 12 Apr 2026 - 21:24

score 226 · Answer 3 · 2026-04-12 11:11:35

226

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Lucas numbers proof

Published on 12 Apr 2026 - 11:11

score 55 · Answer 4 · 2026-04-14 09:59:57

55

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Non inductive proof for square of odd integers

Published on 14 Apr 2026 - 9:59

score 126 · Answer 5 · 2026-04-13 23:22:42

126

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Use induction to show $0< x_n < 3$ and find its limit

Published on 13 Apr 2026 - 23:22

score 133 · Answer 6 · 2026-04-15 23:33:18

133

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Use induction to show $\sum_{j=1}^x (4j - 1) = x(2x+1)$

Published on 15 Apr 2026 - 23:33

score 95 · Answer 7 · 2026-04-16 03:37:25

95

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Prove that $(a^n - b^n) = (a-b) \sum_{i=1}^n a^{i-1} b^{n-i}$

Published on 16 Apr 2026 - 3:37

score 137 · Answer 8 · 2026-04-12 23:39:36

137

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Prove $b-a \le \sum^n_{i=1}(b_i-a_i)$ by induction

Published on 12 Apr 2026 - 23:39

score 338 · Answer 9 · 2026-04-16 16:00:54

338

Views

Prove $\sum _{k=2}^{n} k(k-1) {n \choose k}=n(n-1)2^{n-2}$

Published on 16 Apr 2026 - 16:00

score 17.8k · Answer 10 · 2026-04-15 11:26:11

17.8k

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Induction proof of the identity $\cos x+\cos(2x)+\cdots+\cos (nx) = \frac{\sin(\frac{nx}{2})\cos\frac{(n+1)x}{2}}{\sin(\frac{x}{2})}$

Published on 15 Apr 2026 - 11:26

score 61 · Answer 11 · 2026-04-16 11:52:20

61

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Prove by induction that $I_n = \frac{4^{n+1}n!(n+1)!}{(2n+3)!}$

Published on 16 Apr 2026 - 11:52

score 87 · Answer 12 · 2026-04-14 00:22:26

87

Views

induction with 2 recursive sequnces

Published on 14 Apr 2026 - 0:22

score 92 · Answer 13 · 2026-04-10 00:06:19

92

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How can you prove this by strong induction?

Published on 10 Apr 2026 - 0:06

score 5.1k · Answer 14 · 2026-04-11 14:57:21

5.1k

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Strong Induction Proof of amounts of money

Published on 11 Apr 2026 - 14:57

score 173 · Answer 15 · 2026-04-14 17:51:40

173

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How to prove by induction that $\frac{a^n+b^n}{2}\geq\left(\frac{a+b}{2}\right)^n$?

Published on 14 Apr 2026 - 17:51

List Question

Expanding a Proof of Induction on $\Bbb N $ to $\Bbb Q $ (Linear Algebra)

Prove that the identity is true for all natural numbers

Lucas numbers proof

Non inductive proof for square of odd integers

Use induction to show $0< x_n < 3$ and find its limit

Use induction to show $\sum_{j=1}^x (4j - 1) = x(2x+1)$

Prove that $(a^n - b^n) = (a-b) \sum_{i=1}^n a^{i-1} b^{n-i}$

Prove $b-a \le \sum^n_{i=1}(b_i-a_i)$ by induction

Prove $\sum _{k=2}^{n} k(k-1) {n \choose k}=n(n-1)2^{n-2}$

Induction proof of the identity $\cos x+\cos(2x)+\cdots+\cos (nx) = \frac{\sin(\frac{nx}{2})\cos\frac{(n+1)x}{2}}{\sin(\frac{x}{2})}$

Prove by induction that $I_n = \frac{4^{n+1}n!(n+1)!}{(2n+3)!}$

induction with 2 recursive sequnces

How can you prove this by strong induction?

Strong Induction Proof of amounts of money

How to prove by induction that $\frac{a^n+b^n}{2}\geq\left(\frac{a+b}{2}\right)^n$?

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