Question

Show that the sequence $a_n=\frac{cos(n^2+n)}{n^2}$ converges to $0$.

score 344 · Answer 1 · 2026-03-25 06:30:34

344

Views

Show that the sequence $a_n=\frac{cos(n^2+n)}{n^2}$ converges to $0$.

Published on 25 Mar 2026 - 6:30

score 97 · Answer 2 · 2026-03-25 04:41:08

97

Views

A lack of understanding of convergence in distribution

Published on 25 Mar 2026 - 4:41

score 128 · Answer 3 · 2018-04-12 03:57:05

128

Views

What is the finite sum of an alternating odd sequence with binomial coefficients: $ \ \sum_{k=0}^{j} \binom{j}{k} \ \frac{(-1)^k}{2k+1}$?

Published on 12 Apr 2018 - 3:57

score 134 · Answer 4 · 2026-03-27 12:07:05

134

Views

Convergence of Series correctly determined? (Quotient and Alternating Series Criterions)

Published on 27 Mar 2026 - 12:07

score 693 · Answer 5 · 2026-03-28 02:21:28

693

Views

Stable convergence in distribution

Published on 28 Mar 2026 - 2:21

score 130 · Answer 6 · 2026-03-26 20:41:13

130

Views

Let the sequence be defined recursively $X_{n+1}=pX_{n}+q$ for p nonzero and $X_{1}$ arbitrary. In what conditions does the sequence converge?

Published on 26 Mar 2026 - 20:41

score 44 · Answer 7 · 2018-04-12 15:31:15

Let $r≥1$ be fixed and let $X_n →X$ in $L^r$ and $Y_n →Y$ in $L^r$ as $n→∞$. Show that $X_n + Y_n → X + Y$ in $L^r$ as $n → ∞$

score 555 · Answer 8 · 2018-04-12 19:01:53

555

Views

Sequence of continuous 'tent' functions converging to dirac integral

Published on 12 Apr 2018 - 19:01

score 165 · Answer 9 · 2026-03-25 02:57:40

165

Views

Limit integral switch for nondecreasing functions

Published on 25 Mar 2026 - 2:57

score 234 · Answer 10 · 2026-03-29 14:45:54

234

Views

The topology induced by a "good" net convergence notion induces a net convergence notion as originally specified

Published on 29 Mar 2026 - 14:45

score 29 · Answer 11 · 2026-03-25 03:03:53

29

Views

Set Inclusion Involving Convergence in Measure in Finite Measure Space

Published on 25 Mar 2026 - 3:03

score 129 · Answer 12 · 2026-03-25 21:46:40

129

Views

Show that $X_n$ converge a.s

Published on 25 Mar 2026 - 21:46

score 58 · Answer 13 · 2018-04-13 08:56:05

58

Views

Approximation of integrable function by a step function

Published on 13 Apr 2018 - 8:56

score 104 · Answer 14 · 2026-03-26 06:01:40

104

Views

Convergence of $\sum_{n=1}^\infty\left(\frac{\sqrt{n+1}}{\zeta(n+1)}-\frac{\sqrt{n}}{\zeta(n)}\right)^\lambda$ for a suitable and small $\lambda>0$

Published on 26 Mar 2026 - 6:01

score 140 · Answer 15 · 2026-03-27 02:59:31

140

Views

For which values of m is the improper integral convergent

Published on 27 Mar 2026 - 2:59

List Question

Show that the sequence $a_n=\frac{cos(n^2+n)}{n^2}$ converges to $0$.

A lack of understanding of convergence in distribution

What is the finite sum of an alternating odd sequence with binomial coefficients: $ \ \sum_{k=0}^{j} \binom{j}{k} \ \frac{(-1)^k}{2k+1}$?

Convergence of Series correctly determined? (Quotient and Alternating Series Criterions)

Stable convergence in distribution

Let the sequence be defined recursively $X_{n+1}=pX_{n}+q$ for p nonzero and $X_{1}$ arbitrary. In what conditions does the sequence converge?

Let $r≥1$ be fixed and let $X_n →X$ in $L^r$ and $Y_n →Y$ in $L^r$ as $n→∞$. Show that $X_n + Y_n → X + Y$ in $L^r$ as $n → ∞$

Sequence of continuous 'tent' functions converging to dirac integral

Limit integral switch for nondecreasing functions

The topology induced by a "good" net convergence notion induces a net convergence notion as originally specified

Set Inclusion Involving Convergence in Measure in Finite Measure Space

Show that $X_n$ converge a.s

Approximation of integrable function by a step function

Convergence of $\sum_{n=1}^\infty\left(\frac{\sqrt{n+1}}{\zeta(n+1)}-\frac{\sqrt{n}}{\zeta(n)}\right)^\lambda$ for a suitable and small $\lambda>0$

For which values of m is the improper integral convergent

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