Question

For every n ∈ N, prove that $(1 − 1/2 )(1 − 1/2^2 ). . .(1 − 1/2^n ) ≥ 1/4 + 1/2^{n+1}$ through induction.

score 490 · Answer 1 · 2026-04-17 01:36:40

490

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For every n ∈ N, prove that $(1 − 1/2 )(1 − 1/2^2 ). . .(1 − 1/2^n ) ≥ 1/4 + 1/2^{n+1}$ through induction.

Published on 17 Apr 2026 - 1:36

score 129 · Answer 2 · 2026-04-13 23:11:13

129

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Proof of infinitude of the number of primes of the form $4k+1$

Published on 13 Apr 2026 - 23:11

score 55 · Answer 3 · 2026-04-12 04:32:41

55

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Proof check regarding a simple real analysis problem about the intersections of sets

Published on 12 Apr 2026 - 4:32

score 104 · Answer 4 · 2026-03-29 22:41:21

104

Views

Given independent random variables $X_{k}\sim\text{Poisson}(\lambda_{k})$, what is the distribution of $X_{1} + X_{2} + \ldots + X_{n}$?

Published on 29 Mar 2026 - 22:41

score 82 · Answer 5 · 2026-04-09 07:22:07

82

Views

Regarding L$\to$ rule in sequent calculus and difference between G1$_c$ and G1$_i$ system

Published on 09 Apr 2026 - 7:22

score 1.9k · Answer 6 · 2026-04-16 18:50:56

1.9k

Views

Prove that for every n ∈ Z, there exist a, b ∈ Z such that $n = 5a + 2b$.

Published on 16 Apr 2026 - 18:50

score 77 · Answer 7 · 2026-03-30 15:39:26

77

Views

Moment generating functions and normal distributions

Published on 30 Mar 2026 - 15:39

score 583 · Answer 8 · 2026-03-25 06:04:31

583

Views

A proof that $\langle u,v\mid u^4=v^3=1, uv=v^2u^2\rangle$ defines the trivial group.

Published on 25 Mar 2026 - 6:04

score 22.1k · Answer 9 · 2026-04-10 21:45:01

22.1k

Views

Show that limit does not exist (two variables)

Published on 10 Apr 2026 - 21:45

score 46 · Answer 10 · 2026-04-29 08:19:17

46

Views

Does this double series diverge?

Published on 29 Apr 2026 - 8:19

score 238 · Answer 11 · 2026-03-29 22:34:07

238

Views

Assume that $Z_i\sim\mathcal{N}(0,1)$ are independent and prove that $\sum\limits_{i=1}^{n}(Z_i-\overline{Z})^{2}\sim\chi^{2}_{(n)}$

Published on 29 Mar 2026 - 22:34

score 122 · Answer 12 · 2026-04-12 06:46:29

122

Views

Proof Verification - Elementary proof that $\sqrt3$ is irrational

Published on 12 Apr 2026 - 6:46

score 83 · Answer 13 · 2026-04-10 19:37:19

83

Views

Using Bayes' theorem

Published on 10 Apr 2026 - 19:37

score 54 · Answer 14 · 2026-04-16 08:44:28

54

Views

Verification (and help) with the questions related to convergence of recurrences in the form $x_{n+2} = kx_{n+1} + px_n$

Published on 16 Apr 2026 - 8:44

score 124 · Answer 15 · 2026-04-16 17:13:14

124

Views

Discrete metric space and continuity.

Published on 16 Apr 2026 - 17:13

List Question

For every n ∈ N, prove that $(1 − 1/2 )(1 − 1/2^2 ). . .(1 − 1/2^n ) ≥ 1/4 + 1/2^{n+1}$ through induction.

Proof of infinitude of the number of primes of the form $4k+1$

Proof check regarding a simple real analysis problem about the intersections of sets

Given independent random variables $X_{k}\sim\text{Poisson}(\lambda_{k})$, what is the distribution of $X_{1} + X_{2} + \ldots + X_{n}$?

Regarding L$\to$ rule in sequent calculus and difference between G1$_c$ and G1$_i$ system

Prove that for every n ∈ Z, there exist a, b ∈ Z such that $n = 5a + 2b$.

Moment generating functions and normal distributions

A proof that $\langle u,v\mid u^4=v^3=1, uv=v^2u^2\rangle$ defines the trivial group.

Show that limit does not exist (two variables)

Does this double series diverge?

Assume that $Z_i\sim\mathcal{N}(0,1)$ are independent and prove that $\sum\limits_{i=1}^{n}(Z_i-\overline{Z})^{2}\sim\chi^{2}_{(n)}$

Proof Verification - Elementary proof that $\sqrt3$ is irrational

Using Bayes' theorem

Verification (and help) with the questions related to convergence of recurrences in the form $x_{n+2} = kx_{n+1} + px_n$

Discrete metric space and continuity.

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