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Prove by induction: $\sum_{i=0}^{n-1}\frac{i}{2^i}=2-\frac{n+1}{2^{n-1}}$

score 190 · Answer 1 · 2026-04-17 02:41:13

190

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Prove by induction: $\sum_{i=0}^{n-1}\frac{i}{2^i}=2-\frac{n+1}{2^{n-1}}$

Published on 17 Apr 2026 - 2:41

score 658 · Answer 2 · 2026-04-15 14:37:26

658

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Need help Proving that If $D=P^{-1}AP$ then $A^m = PD^mP^{-1}.$

Published on 15 Apr 2026 - 14:37

score 467 · Answer 3 · 2026-04-17 09:42:05

467

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Please verify my induction proof: $3$| $(5 \cdot 10^{n+1} + 3\cdot 10^n + 4)$ for $n ∈ \mathbb N $

Published on 17 Apr 2026 - 9:42

score 52 · Answer 4 · 2026-04-15 10:49:27

52

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Show inequality (probably using the induction)

Published on 15 Apr 2026 - 10:49

score 73 · Answer 5 · 2026-04-15 16:23:46

73

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Prove inequality by induction $\forall n \in \mathbb{N}, n\ge 2 \ \ : \ \ (1+\frac1n)^n<\sum\limits_{k=0}^n \frac1{k!}<3$

Published on 15 Apr 2026 - 16:23

score 272 · Answer 6 · 2026-04-11 19:47:56

272

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Multivariate complex Gaussian integral proof by induction on matrix dimension.

Published on 11 Apr 2026 - 19:47

score 59 · Answer 7 · 2026-04-16 14:05:25

59

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How many elements has S(M,M)?

Published on 16 Apr 2026 - 14:05

score 49 · Answer 8 · 2026-04-14 04:13:45

49

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how to find every n>2 where 8 + 5^(n-3) + 3^(n-3) that are divisible by 8 (using induction)

Published on 14 Apr 2026 - 4:13

score 43 · Answer 9 · 2026-04-13 05:33:04

43

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Help proving the countability of a set

Published on 13 Apr 2026 - 5:33

score 2.9k · Answer 10 · 2026-04-12 08:33:11

2.9k

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Proof by induction of Complex Numbers $(Z^n)^=(Z^)^n$

Published on 12 Apr 2026 - 8:33

score 147 · Answer 11 · 2026-04-15 09:17:14

147

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Inductive proof that $2^n $ is bigger or equal to $1+n$

Published on 15 Apr 2026 - 9:17

score 20 · Answer 12 · 2026-04-15 23:56:55

20

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Mathematical Induction question Using $n\ge t\ge 0$

Published on 15 Apr 2026 - 23:56

score 180 · Answer 13 · 2026-03-25 07:47:31

180

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Induction, coinduction, and ordinal induction

Published on 25 Mar 2026 - 7:47

score 57 · Answer 14 · 2026-04-17 15:40:21

57

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induction, n + 2

Published on 17 Apr 2026 - 15:40

score 116 · Answer 15 · 2026-04-17 01:36:03

116

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Solve by induction, $(x+1)^2+(x+2)^2...(2x)^2$.

Published on 17 Apr 2026 - 1:36

List Question

Prove by induction: $\sum_{i=0}^{n-1}\frac{i}{2^i}=2-\frac{n+1}{2^{n-1}}$

Need help Proving that If $D=P^{-1}AP$ then $A^m = PD^mP^{-1}.$

Please verify my induction proof: $3$| $(5 \cdot 10^{n+1} + 3\cdot 10^n + 4)$ for $n ∈ \mathbb N $

Show inequality (probably using the induction)

Prove inequality by induction $\forall n \in \mathbb{N}, n\ge 2 \ \ : \ \ (1+\frac1n)^n<\sum\limits_{k=0}^n \frac1{k!}<3$

Multivariate complex Gaussian integral proof by induction on matrix dimension.

How many elements has S(M,M)?

how to find every n>2 where 8 + 5^(n-3) + 3^(n-3) that are divisible by 8 (using induction)

Help proving the countability of a set

Proof by induction of Complex Numbers $(Z^n)^=(Z^)^n$

Inductive proof that $2^n $ is bigger or equal to $1+n$

Mathematical Induction question Using $n\ge t\ge 0$

Induction, coinduction, and ordinal induction

induction, n + 2

Solve by induction, $(x+1)^2+(x+2)^2...(2x)^2$.

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