Question

Prove that $ \frac{1}{15} + \frac{1}{27} + \frac{1}{3*9}+... = \frac{8}{9} - \frac{2}{3}\ln(2) $

score 73 · Answer 1 · 2026-04-17 05:25:14

73

Views

Prove that $ \frac{1}{15} + \frac{1}{27} + \frac{1}{3*9}+... = \frac{8}{9} - \frac{2}{3}\ln(2) $

Published on 17 Apr 2026 - 5:25

score 31 · Answer 2 · 2026-04-16 11:10:12

31

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For $w \in L^{p}((s,t) ; X), 1 \leq p \lt \infty$, the mollification $J_{h}[w] \rightarrow w$, as $h \rightarrow 0$, in $ L^{p}((s,t) ; X)$.

Published on 16 Apr 2026 - 11:10

score 46 · Answer 3 · 2026-04-15 14:28:16

46

Views

Looking for a convergent sequence in $W^{1,2}[0,\infty)$ with some properties.

Published on 15 Apr 2026 - 14:28

score 59 · Answer 4 · 2026-04-12 21:33:58

59

Views

Question on convergence of a formula for a zero-mean q-periodic Dirichlet series

Published on 12 Apr 2026 - 21:33

score 75 · Answer 5 · 2026-04-15 19:46:07

75

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Find a condition on the $a_{n}$ that guarantees the series $\sum_{i=0}^{^\infty} a_{n}X_{n}$ is almost surely convergent,

Published on 15 Apr 2026 - 19:46

score 219 · Answer 6 · 2026-04-14 15:39:14

219

Views

Lebesgue's Dominated Convergence Theorem $(g-f)$ is finite, is well defined?

Published on 14 Apr 2026 - 15:39

score 264 · Answer 7 · 2026-04-16 08:53:28

264

Views

Converging or Diverging function?

Published on 16 Apr 2026 - 8:53

score 46 · Answer 8 · 2026-04-16 10:18:10

46

Views

Set $s_n$ to be a sequence so that $|s_{n+1}-s_n|\le\frac{1}{n^p}$ for all $n \in \mathbb{N}$

Published on 16 Apr 2026 - 10:18

score 161 · Answer 9 · 2026-04-15 18:30:59

161

Views

Does the recurring succession $X_{n+1} = 1+\frac{1}{X_n}$ converge?

Published on 15 Apr 2026 - 18:30

score 126 · Answer 10 · 2026-04-16 20:54:43

126

Views

Proving that a sequence converge to $\sqrt{2}$

Published on 16 Apr 2026 - 20:54

score 66 · Answer 11 · 2026-04-11 05:23:55

66

Views

Is the functional mapping $x$ to the statistical limit of $x$ bounded (continuous)?

Published on 11 Apr 2026 - 5:23

score 253 · Answer 12 · 2026-04-17 06:12:29

253

Views

Convergence of the sequence $x_n = \sqrt{x_{n-1}x_{n-2}}$ for all $n\geq3$

Published on 17 Apr 2026 - 6:12

score 212 · Answer 13 · 2026-04-14 21:49:38

212

Views

Is $\sum_{n=1}^{+ \infty}\left(\frac {1}{n}-\frac{1}{p_n}\right)$ convergent?

Published on 14 Apr 2026 - 21:49

score 23 · Answer 14 · 2026-04-11 10:18:52

23

Views

Convergence within a metric space with different starting points

Published on 11 Apr 2026 - 10:18

score 259 · Answer 15 · 2026-04-15 00:09:29

259

Views

Question on convergence of a formula for the Dirichlet eta function $\eta(s)=(1-2^{1-s})\,\zeta(s)$

Published on 15 Apr 2026 - 0:09

List Question

Prove that $ \frac{1}{15} + \frac{1}{27} + \frac{1}{3*9}+... = \frac{8}{9} - \frac{2}{3}\ln(2) $

For $w \in L^{p}((s,t) ; X), 1 \leq p \lt \infty$, the mollification $J_{h}[w] \rightarrow w$, as $h \rightarrow 0$, in $ L^{p}((s,t) ; X)$.

Looking for a convergent sequence in $W^{1,2}[0,\infty)$ with some properties.

Question on convergence of a formula for a zero-mean q-periodic Dirichlet series

Find a condition on the $a_{n}$ that guarantees the series $\sum_{i=0}^{^\infty} a_{n}X_{n}$ is almost surely convergent,

Lebesgue's Dominated Convergence Theorem $(g-f)$ is finite, is well defined?

Converging or Diverging function?

Set $s_n$ to be a sequence so that $|s_{n+1}-s_n|\le\frac{1}{n^p}$ for all $n \in \mathbb{N}$

Does the recurring succession $X_{n+1} = 1+\frac{1}{X_n}$ converge?

Proving that a sequence converge to $\sqrt{2}$

Is the functional mapping $x$ to the statistical limit of $x$ bounded (continuous)?

Convergence of the sequence $x_n = \sqrt{x_{n-1}x_{n-2}}$ for all $n\geq3$

Is $\sum_{n=1}^{+ \infty}\left(\frac {1}{n}-\frac{1}{p_n}\right)$ convergent?

Convergence within a metric space with different starting points

Question on convergence of a formula for the Dirichlet eta function $\eta(s)=(1-2^{1-s})\,\zeta(s)$

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