Question

Prove that $\{S_n - [S_n]\}$ is dense on the interval $[0,1)$ when $S_n$ is $\sum_{k=1}^n b_k$.

score 218 · Answer 1 · 2026-04-24 20:59:02

218

Views

Prove that $\{S_n - [S_n]\}$ is dense on the interval $[0,1)$ when $S_n$ is $\sum_{k=1}^n b_k$.

Published on 24 Apr 2026 - 20:59

score 232 · Answer 2 · 2026-04-15 19:30:47

232

Views

New/useful method for summation of divergent series?

Published on 15 Apr 2026 - 19:30

score 118 · Answer 3 · 2026-04-16 06:27:36

118

Views

Let $a_{n}$ be a sequence as $|a_{n+1}-a_{n}|\leq\frac{\ln(n+1)}{n^{2}}$ for every $n\in\mathbb{N}$. Prove that $a_{n}$ converges.

Published on 16 Apr 2026 - 6:27

score 52 · Answer 4 · 2026-04-15 23:51:30

52

Views

Why isn't $< \{ 1\} \{2 \}>$ contained in $< \{1,2\} \{3,4\}>$?

Published on 15 Apr 2026 - 23:51

score 677 · Answer 5 · 2026-04-12 19:36:32

677

Views

Questions about proof of Raabe's test in Wikipedia

Published on 12 Apr 2026 - 19:36

score 356 · Answer 6 · 2026-04-15 12:14:28

356

Views

Can numbers with similar stopping times in the Collatz Conjecture be functionally described?

Published on 15 Apr 2026 - 12:14

score 36 · Answer 7 · 2026-04-24 20:59:01

36

Views

Properties of a succession of functions while knowing the value of its series

Published on 24 Apr 2026 - 20:59

score 27 · Answer 8 · 2026-04-17 00:38:22

Rewrite $\left\vert\sum_{k\in B} \exp\left(\frac{2\pi ijk}{p} \right)\right\vert^2$, where $p$ is a prime $\ge 3$ and $B \subset \{1,2,...,p-1\}$.

score 67 · Answer 9 · 2026-04-10 19:07:46

67

Views

Alternating series that is bounded by 1 but fails an alternating series test

Published on 10 Apr 2026 - 19:07

score 1.4k · Answer 10 · 2026-04-16 01:53:49

1.4k

Views

Nested Sequence of Closed Bounded Sets in a Complete Metric Space

Published on 16 Apr 2026 - 1:53

score 254 · Answer 11 · 2026-04-29 12:49:55

254

Views

Additive basis of order $2$ (I)

Published on 29 Apr 2026 - 12:49

score 681 · Answer 12 · 2026-04-29 12:50:08

681

Views

Series whose Cauchy product is absolutely convergent - A general example

Published on 29 Apr 2026 - 12:50

score 62 · Answer 13 · 2026-04-13 15:25:15

62

Views

How do I finish this proof proving the divergence of the harmonic series?

Published on 13 Apr 2026 - 15:25

score 55 · Answer 14 · 2026-04-12 20:03:20

55

Views

Stirling approximation of logarithms

Published on 12 Apr 2026 - 20:03

score 159 · Answer 15 · 2026-04-24 06:36:27

159

Views

How to compute $\prod_{1\le i\le n} \left(1-\frac{1}{2^i}\right)$

Published on 24 Apr 2026 - 6:36

List Question

Prove that $\{S_n - [S_n]\}$ is dense on the interval $[0,1)$ when $S_n$ is $\sum_{k=1}^n b_k$.

New/useful method for summation of divergent series?

Let $a_{n}$ be a sequence as $|a_{n+1}-a_{n}|\leq\frac{\ln(n+1)}{n^{2}}$ for every $n\in\mathbb{N}$. Prove that $a_{n}$ converges.

Why isn't $< \{ 1\} \{2 \}>$ contained in $< \{1,2\} \{3,4\}>$?

Questions about proof of Raabe's test in Wikipedia

Can numbers with similar stopping times in the Collatz Conjecture be functionally described?

Properties of a succession of functions while knowing the value of its series

Rewrite $\left\vert\sum_{k\in B} \exp\left(\frac{2\pi ijk}{p} \right)\right\vert^2$, where $p$ is a prime $\ge 3$ and $B \subset \{1,2,...,p-1\}$.

Alternating series that is bounded by 1 but fails an alternating series test

Nested Sequence of Closed Bounded Sets in a Complete Metric Space

Additive basis of order $2$ (I)

Series whose Cauchy product is absolutely convergent - A general example

How do I finish this proof proving the divergence of the harmonic series?

Stirling approximation of logarithms

How to compute $\prod_{1\le i\le n} \left(1-\frac{1}{2^i}\right)$

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