Question

Sequence $(f_n) \to f_n$ on $S \subseteq \mathbb{R}$ converges uniformly iff $\lim_{n \to \infty} \sup \{f(x)-f_n(x)| : x\in S\} = 0$

score 106 · Answer 1 · 2026-03-26 01:12:44

106

Views

Sequence $(f_n) \to f_n$ on $S \subseteq \mathbb{R}$ converges uniformly iff $\lim_{n \to \infty} \sup \{f(x)-f_n(x)| : x\in S\} = 0$

Published on 26 Mar 2026 - 1:12

score 63 · Answer 2 · 2026-03-27 22:03:50

63

Views

Does this series diverge or converge?

Published on 27 Mar 2026 - 22:03

score 38 · Answer 3 · 2026-03-26 01:12:42

38

Views

What is the rate of convergence of the argmins of a sequence of uniformly convergent strictly convex functions?

Published on 26 Mar 2026 - 1:12

score 102 · Answer 4 · 2018-11-09 19:13:09

102

Views

Prove that the sequence $\{x_n\}$ converges, where: $x_n = 2^n \sin\left(\frac{\pi}{2^{n+1}}\right)$

Published on 09 Nov 2018 - 19:13

score 146 · Answer 5 · 2018-11-09 20:31:28

146

Views

Check almost sure convergence

Published on 09 Nov 2018 - 20:31

score 65 · Answer 6 · 2018-11-10 07:53:01

65

Views

Could I substitute $i$ in a convergence series?

Published on 10 Nov 2018 - 7:53

score 427 · Answer 7 · 2026-03-29 18:37:21

427

Views

If $u_1=4$ and $u_{n+1}=\frac{3u_n+5}{u_n-1}$, then $u_n$ approaches $a=5$ as $n\to\infty$. Show that, if $u_n>a$, then $u_{n+1}<u_n$.

Published on 29 Mar 2026 - 18:37

score 58 · Answer 8 · 2026-03-27 23:48:11

58

Views

If $\big\{n(k);k\in \mathbb{N}\big\}$ be set of all natural numbers none of whose digits is $6$, does $\frac1{n(1)}+\frac1{n(2)}+\ldots$ converge?

Published on 27 Mar 2026 - 23:48

score 99 · Answer 9 · 2018-11-10 12:26:11

99

Views

Prove that $X_n \to c$ (in distribution) $⇒ X_n → c$ (in probability)

Published on 10 Nov 2018 - 12:26

score 522 · Answer 10 · 2026-03-25 08:09:40

522

Views

Sequence of random variables that converges in distribution but whose variances does not converge to limit's variance

Published on 25 Mar 2026 - 8:09

score 41 · Answer 11 · 2026-04-07 23:40:33

41

Views

What does the following sum converge to? is there a closed-form formula?

Published on 07 Apr 2026 - 23:40

score 167 · Answer 12 · 2026-02-23 02:59:23

167

Views

Convergence in Distribution implies Convergence in Expectation uniformly for an equicontinuous family

Published on 23 Feb 2026 - 2:59

score 851 · Answer 13 · 2018-11-11 14:20:08

851

Views

Convergence in Probability is equivalent to "Cauchy in Probability"

Published on 11 Nov 2018 - 14:20

score 1.1k · Answer 14 · 2018-11-11 14:43:21

1.1k

Views

Proving that a sequence [$a_n = \frac{v_n}{n},\; n \ge 2$] converges.

Published on 11 Nov 2018 - 14:43

score 282 · Answer 15 · 2026-04-01 07:48:36

282

Views

Almost sure convergence exercise

Published on 01 Apr 2026 - 7:48

List Question

Sequence $(f_n) \to f_n$ on $S \subseteq \mathbb{R}$ converges uniformly iff $\lim_{n \to \infty} \sup \{f(x)-f_n(x)| : x\in S\} = 0$

Does this series diverge or converge?

What is the rate of convergence of the argmins of a sequence of uniformly convergent strictly convex functions?

Prove that the sequence $\{x_n\}$ converges, where: $x_n = 2^n \sin\left(\frac{\pi}{2^{n+1}}\right)$

Check almost sure convergence

Could I substitute $i$ in a convergence series?

If $u_1=4$ and $u_{n+1}=\frac{3u_n+5}{u_n-1}$, then $u_n$ approaches $a=5$ as $n\to\infty$. Show that, if $u_n>a$, then $u_{n+1}<u_n$.

If $\big\{n(k);k\in \mathbb{N}\big\}$ be set of all natural numbers none of whose digits is $6$, does $\frac1{n(1)}+\frac1{n(2)}+\ldots$ converge?

Prove that $X_n \to c$ (in distribution) $⇒ X_n → c$ (in probability)

Sequence of random variables that converges in distribution but whose variances does not converge to limit's variance

What does the following sum converge to? is there a closed-form formula?

Convergence in Distribution implies Convergence in Expectation uniformly for an equicontinuous family

Convergence in Probability is equivalent to "Cauchy in Probability"

Proving that a sequence [$a_n = \frac{v_n}{n},\; n \ge 2$] converges.

Almost sure convergence exercise

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