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problem proof of induction $2\cdot3^0+2\cdot3^1+2\cdot3^2+...+2\cdot3^{n-1}=3^n-1$

score 55 · Answer 1 · 2026-04-15 03:09:00

55

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problem proof of induction $2\cdot3^0+2\cdot3^1+2\cdot3^2+...+2\cdot3^{n-1}=3^n-1$

Published on 15 Apr 2026 - 3:09

score 81 · Answer 2 · 2026-04-14 19:08:05

81

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Show $ \begin{bmatrix} a & -b \\ b & a \end{bmatrix}^k = \begin{bmatrix} Re((a+ib)^k) & -Im((a+ib)^k) \\ Im((a+ib)^k) & Re((a+ib)^k) \end{bmatrix}$

Published on 14 Apr 2026 - 19:08

score 131 · Answer 3 · 2026-04-11 01:10:30

131

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Why proof by induction is working.

Published on 11 Apr 2026 - 1:10

score 141 · Answer 4 · 2026-04-14 18:22:12

141

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Proving $n! > n^2$ by mathematical induction

Published on 14 Apr 2026 - 18:22

score 4.4k · Answer 5 · 2026-04-16 22:45:52

4.4k

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Proving $a^n-b^n=(a-b)\sum_{k=1}^{n}a^{n-k} b^{k-1}$ with induction

Published on 16 Apr 2026 - 22:45

score 184 · Answer 6 · 2026-04-17 00:29:30

184

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Prove $\frac{1\cdot 3\cdot 5\cdots (2n - 1)}{ 2^n(n + 1)!}\cdot 4^n= \frac{1}{n+1} {2n\choose n}$

Published on 17 Apr 2026 - 0:29

score 1.9k · Answer 7 · 2026-04-14 10:09:00

1.9k

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GCD induction proof

Published on 14 Apr 2026 - 10:09

score 80 · Answer 8 · 2026-04-15 16:07:28

80

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Showing that the $n$th derivative of this piecewise function vanishes at $0$

Published on 15 Apr 2026 - 16:07

score 284 · Answer 9 · 2026-04-16 03:52:59

284

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Proving that $n \leq m^{2} \leq 2n$ by induction

Published on 16 Apr 2026 - 3:52

score 120 · Answer 10 · 2026-04-12 04:34:05

120

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Proof of the well ordering principle without mathematical induction

Published on 12 Apr 2026 - 4:34

score 48 · Answer 11 · 2026-04-14 16:14:21

48

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Prove by induction that this sum is not a natural number.

Published on 14 Apr 2026 - 16:14

score 293 · Answer 12 · 2026-04-16 20:54:32

293

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Proving $\prod_{i=2}^{i=n} \left(1-\frac{1}{i^2}\right) = \frac{n+1}{2n}$ by induction

Published on 16 Apr 2026 - 20:54

score 87 · Answer 13 · 2026-04-15 17:53:47

87

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Please explain this basic proof

Published on 15 Apr 2026 - 17:53

score 121 · Answer 14 · 2026-04-16 09:55:21

121

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Prove $5 \mid (3^{4n} - 1)$ by induction

Published on 16 Apr 2026 - 9:55

score 359 · Answer 15 · 2026-04-12 02:49:10

359

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Proving a Recursive Definition using Induction

Published on 12 Apr 2026 - 2:49

List Question

problem proof of induction $2\cdot3^0+2\cdot3^1+2\cdot3^2+...+2\cdot3^{n-1}=3^n-1$

Show $ \begin{bmatrix} a & -b \\ b & a \end{bmatrix}^k = \begin{bmatrix} Re((a+ib)^k) & -Im((a+ib)^k) \\ Im((a+ib)^k) & Re((a+ib)^k) \end{bmatrix}$

Why proof by induction is working.

Proving $n! > n^2$ by mathematical induction

Proving $a^n-b^n=(a-b)\sum_{k=1}^{n}a^{n-k} b^{k-1}$ with induction

Prove $\frac{1\cdot 3\cdot 5\cdots (2n - 1)}{ 2^n(n + 1)!}\cdot 4^n= \frac{1}{n+1} {2n\choose n}$

GCD induction proof

Showing that the $n$th derivative of this piecewise function vanishes at $0$

Proving that $n \leq m^{2} \leq 2n$ by induction

Proof of the well ordering principle without mathematical induction

Prove by induction that this sum is not a natural number.

Proving $\prod_{i=2}^{i=n} \left(1-\frac{1}{i^2}\right) = \frac{n+1}{2n}$ by induction

Please explain this basic proof

Prove $5 \mid (3^{4n} - 1)$ by induction

Proving a Recursive Definition using Induction

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