Question

Prove $\sum_{n=1}^\infty(\frac{1}{a_{2n-1}}-\frac{1}{a_{2n}})$ convergent

score 81 · Answer 1 · 2021-05-25 14:53:39

81

Views

Prove $\sum_{n=1}^\infty(\frac{1}{a_{2n-1}}-\frac{1}{a_{2n}})$ convergent

Published on 25 May 2021 - 14:53

score 102 · Answer 2 · 2021-05-27 03:30:17

102

Views

Show that sequence of antiderivatives has a subsequence that converges pointwise

Published on 27 May 2021 - 3:30

score 88 · Answer 3 · 2021-05-27 12:43:19

88

Views

$f_n\rightarrow f$ uniformly in an interval

Published on 27 May 2021 - 12:43

score 28 · Answer 4 · 2021-05-27 18:57:31

28

Views

Uniform convergence of the sequence of functions: $g_n(x) = \sum_{k=2}^n \frac{(-1)^k}{k\ln(k)}f(kx)$.

Published on 27 May 2021 - 18:57

score 97 · Answer 5 · 2021-05-27 23:38:45

97

Views

behaviour of sequence of bounded real functions $f_n$ converging uniformly to $f$

Published on 27 May 2021 - 23:38

score 76 · Answer 6 · 2021-06-01 13:03:31

76

Views

Proving $f_n(x)$ not uniformly convergent

Published on 01 Jun 2021 - 13:03

score 178 · Answer 7 · 2021-06-02 07:32:33

178

Views

Show uniform convergence of sequence of functions $f_n(x)=x^n$ on $[0,0.9]$

Published on 02 Jun 2021 - 7:32

score 84 · Answer 8 · 2021-06-02 09:28:07

84

Views

Monotone convergence theorem (proof with Darboux sum)

Published on 02 Jun 2021 - 9:28

score 469 · Answer 9 · 2021-06-02 17:43:57

469

Views

Uniform convergence of the sum $\sum_{n=0}^\infty {(n+1)x^n}$, $|x| < 1$

Published on 02 Jun 2021 - 17:43

score 108 · Answer 10 · 2021-06-02 22:27:58

108

Views

Monotonicity of sequence of functions - Dini's theorem

Published on 02 Jun 2021 - 22:27

score 73 · Answer 11 · 2021-06-07 16:41:19

73

Views

Does $f_n(x)=\sin(x)^{1/n}$ uniformly converge in $I=[\frac {\pi}{4},\frac {3\pi}{4}]$

Published on 07 Jun 2021 - 16:41

score 61 · Answer 12 · 2021-06-08 11:25:54

61

Views

Finding $\lim_{N\to\infty}\int_{0}^{\infty}1-\left(1-\exp\left(-x^2\right)\right)^{N}\text{d}x$

Published on 08 Jun 2021 - 11:25

score 41 · Answer 13 · 2021-06-14 07:20:09

41

Views

Theorem about series of functions

Published on 14 Jun 2021 - 7:20

score 134 · Answer 14 · 2021-06-15 14:28:54

134

Views

Show that $\frac{1}{f_{n}}$ converges uniformly to $\frac{1}{f}$ given the following

Published on 15 Jun 2021 - 14:28

score 437 · Answer 15 · 2021-06-18 15:41:38

437

Views

If $f:B\to\mathbb{R},\ B\subset\mathbb{R}$ is increasing then there is a sequence of strictly increasing functions whose pointwise limit is $f$

Published on 18 Jun 2021 - 15:41

List Question

Prove $\sum_{n=1}^\infty(\frac{1}{a_{2n-1}}-\frac{1}{a_{2n}})$ convergent

Show that sequence of antiderivatives has a subsequence that converges pointwise

$f_n\rightarrow f$ uniformly in an interval

Uniform convergence of the sequence of functions: $g_n(x) = \sum_{k=2}^n \frac{(-1)^k}{k\ln(k)}f(kx)$.

behaviour of sequence of bounded real functions $f_n$ converging uniformly to $f$

Proving $f_n(x)$ not uniformly convergent

Show uniform convergence of sequence of functions $f_n(x)=x^n$ on $[0,0.9]$

Monotone convergence theorem (proof with Darboux sum)

Uniform convergence of the sum $\sum_{n=0}^\infty {(n+1)x^n}$, $|x| < 1$

Monotonicity of sequence of functions - Dini's theorem

Does $f_n(x)=\sin(x)^{1/n}$ uniformly converge in $I=[\frac {\pi}{4},\frac {3\pi}{4}]$

Finding $\lim_{N\to\infty}\int_{0}^{\infty}1-\left(1-\exp\left(-x^2\right)\right)^{N}\text{d}x$

Theorem about series of functions

Show that $\frac{1}{f_{n}}$ converges uniformly to $\frac{1}{f}$ given the following

If $f:B\to\mathbb{R},\ B\subset\mathbb{R}$ is increasing then there is a sequence of strictly increasing functions whose pointwise limit is $f$

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