Question

Is there a sense in which this limit is zero?

score 193 · Answer 1 · 2026-04-09 11:57:08

193

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Is there a sense in which this limit is zero?

Published on 09 Apr 2026 - 11:57

score 120 · Answer 2 · 2026-04-09 13:02:30

120

Views

If $(a_{n})_{n}$ is a bounded sequence, show that $\liminf_{n\to \infty}a_{n}\leq \liminf_{n\to \infty}\frac{a_{1}+a_{2}+\cdots +a_{n}}{n}$.

Published on 09 Apr 2026 - 13:02

score 299 · Answer 3 · 2026-03-26 17:32:12

299

Views

Prove that Tr(B) is rank(B) if B is any 2x2 matrix such that $B^2 = B$

Published on 26 Mar 2026 - 17:32

score 205 · Answer 4 · 2026-03-25 06:01:54

205

Views

Proving that a specific string in in a set of strings

Published on 25 Mar 2026 - 6:01

score 1k · Answer 5 · 2026-04-09 01:55:15

1k

Views

Integer programming proof: If an LP is unbounded then the IP is unbounded

Published on 09 Apr 2026 - 1:55

score 118 · Answer 6 · 2026-04-08 22:27:31

118

Views

Prove the fact that two integrals are equal

Published on 08 Apr 2026 - 22:27

score 166 · Answer 7 · 2026-04-09 03:40:57

166

Views

Prove that $\sum_{i=1}^n\lvert[a_i]\rvert$ is even iff $n$ is even

Published on 09 Apr 2026 - 3:40

score 53 · Answer 8 · 2026-04-09 16:53:19

53

Views

Interior is always open verification

Published on 09 Apr 2026 - 16:53

score 103 · Answer 9 · 2026-04-09 00:05:18

103

Views

How to prove this delta-epsilon proof?

Published on 09 Apr 2026 - 0:05

score 407 · Answer 10 · 2026-04-09 03:39:10

407

Views

How to prove this delta-epsilon proof involving $x^2$?

Published on 09 Apr 2026 - 3:39

score 532 · Answer 11 · 2026-04-09 00:31:27

532

Views

How to prove by induction that a string is a member of a recursively defined language?

Published on 09 Apr 2026 - 0:31

score 68 · Answer 12 · 2026-03-25 09:29:03

68

Views

Proof that $x_1=x_2$ maximizes $f(x_1)+f(x_2)$, when its derivatives are unequal until $x_1=x_2$.

Published on 25 Mar 2026 - 9:29

score 5.9k · Answer 13 · 2018-01-23 23:29:53

5.9k

Views

How to prove rigorously that the series $1/(3n)$ diverges

Published on 23 Jan 2018 - 23:29

score 75 · Answer 14 · 2026-03-25 11:07:00

75

Views

Proof verification: $\forall x \in [\frac{\pi}{2}, \pi], sin(x) - cos(x) \geq 1$.

Published on 25 Mar 2026 - 11:07

score 112 · Answer 15 · 2026-04-09 02:09:33

112

Views

Proof by contrapositive: $x^4 + 2x^2 - 2x \lt 0 \Rightarrow 0 \lt x \lt 1$

Published on 09 Apr 2026 - 2:09

List Question

Is there a sense in which this limit is zero?

If $(a_{n})_{n}$ is a bounded sequence, show that $\liminf_{n\to \infty}a_{n}\leq \liminf_{n\to \infty}\frac{a_{1}+a_{2}+\cdots +a_{n}}{n}$.

Prove that Tr(B) is rank(B) if B is any 2x2 matrix such that $B^2 = B$

Proving that a specific string in in a set of strings

Integer programming proof: If an LP is unbounded then the IP is unbounded

Prove the fact that two integrals are equal

Prove that $\sum_{i=1}^n\lvert[a_i]\rvert$ is even iff $n$ is even

Interior is always open verification

How to prove this delta-epsilon proof?

How to prove this delta-epsilon proof involving $x^2$?

How to prove by induction that a string is a member of a recursively defined language?

Proof that $x_1=x_2$ maximizes $f(x_1)+f(x_2)$, when its derivatives are unequal until $x_1=x_2$.

How to prove rigorously that the series $1/(3n)$ diverges

Proof verification: $\forall x \in [\frac{\pi}{2}, \pi], sin(x) - cos(x) \geq 1$.

Proof by contrapositive: $x^4 + 2x^2 - 2x \lt 0 \Rightarrow 0 \lt x \lt 1$

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