Question

Closed Form For $n$ Consecutive Summations

score 54 · Answer 1 · 2026-03-25 04:54:42

54

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Closed Form For $n$ Consecutive Summations

Published on 25 Mar 2026 - 4:54

score 24 · Answer 2 · 2018-04-14 10:30:37

24

Views

Generating $n$ numbers whose random subsum equals zero

Published on 14 Apr 2018 - 10:30

score 58 · Answer 3 · 2026-03-25 04:55:47

58

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Closed form of basic looking geometric-like sum

Published on 25 Mar 2026 - 4:55

score 261 · Answer 4 · 2026-03-25 06:06:31

261

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How many $m$ such that : $\sum\limits_{k=1}^m \left\lfloor\frac{m}{k}\right\rfloor$ be even?

Published on 25 Mar 2026 - 6:06

score 117 · Answer 5 · 2026-03-26 17:33:30

117

Views

Suppose $(a)_{j=1}^{\infty}$ is a sequence of real numbers. prove by induction on n that $|\sum_{j=1}^{n}a_j|\leq\sum_{j=1}^{n}|a_j|$

Published on 26 Mar 2026 - 17:33

score 442 · Answer 6 · 2026-03-26 04:52:37

442

Views

Confusion about proof involving sums and binomial coefficients

Published on 26 Mar 2026 - 4:52

score 36 · Answer 7 · 2026-03-26 03:13:36

36

Views

Prove $\binom{n}{1} - \frac{1}{2}\binom{n}{2} + \frac{1}{3}\binom{n}{3} + \ldots = 1 + \frac{1}{2} + \frac{1}{3} + \ldots + \frac{1}{n}$

Published on 26 Mar 2026 - 3:13

score 1.8k · Answer 8 · 2026-03-26 17:34:51

1.8k

Views

Formula for $\sum_{k=1}^n k2^k$

Published on 26 Mar 2026 - 17:34

score 116 · Answer 9 · 2018-04-16 11:22:53

116

Views

$\sum_{H \in \mathscr H} 1_H(\omega) = 1$

Published on 16 Apr 2018 - 11:22

score 281 · Answer 10 · 2026-03-25 04:41:47

281

Views

$\sum_{n=0}^\infty\exp(-\varepsilon_n / \tau) =\frac{\pi}{2}\int_0^\infty\exp(-\varepsilon_n/\tau) n dn$

Published on 25 Mar 2026 - 4:41

score 443 · Answer 11 · 2026-03-26 14:35:01

443

Views

Sum of the first n terms of series $\frac{x^{3n}}{3n(3n-1)(3n-2)}$

Published on 26 Mar 2026 - 14:35

score 55 · Answer 12 · 2018-04-16 21:06:54

55

Views

Expressing summation as integral.

Published on 16 Apr 2018 - 21:06

score 170 · Answer 13 · 2018-04-17 05:06:57

170

Views

Show that the set $A$ contains an open interval.

Published on 17 Apr 2018 - 5:06

score 323 · Answer 14 · 2026-03-25 19:05:09

323

Views

Evaluate $\sum_{n=1}^\infty (-1)^{n+1}({1 - \cos(2n-1) \over 2n-1})$ using Fourier Series

Published on 25 Mar 2026 - 19:05

score 1.1k · Answer 15 · 2018-04-17 16:33:50

1.1k

Views

Evaluate $\lim_{n\to \infty} \left( \sum_{r=0}^n \frac {2^r}{5^{2^r}+1}\right) $

Published on 17 Apr 2018 - 16:33

List Question

Closed Form For $n$ Consecutive Summations

Generating $n$ numbers whose random subsum equals zero

Closed form of basic looking geometric-like sum

How many $m$ such that : $\sum\limits_{k=1}^m \left\lfloor\frac{m}{k}\right\rfloor$ be even?

Suppose $(a)_{j=1}^{\infty}$ is a sequence of real numbers. prove by induction on n that $|\sum_{j=1}^{n}a_j|\leq\sum_{j=1}^{n}|a_j|$

Confusion about proof involving sums and binomial coefficients

Prove $\binom{n}{1} - \frac{1}{2}\binom{n}{2} + \frac{1}{3}\binom{n}{3} + \ldots = 1 + \frac{1}{2} + \frac{1}{3} + \ldots + \frac{1}{n}$

Formula for $\sum_{k=1}^n k2^k$

$\sum_{H \in \mathscr H} 1_H(\omega) = 1$

$\sum_{n=0}^\infty\exp(-\varepsilon_n / \tau) =\frac{\pi}{2}\int_0^\infty\exp(-\varepsilon_n/\tau) n dn$

Sum of the first n terms of series $\frac{x^{3n}}{3n(3n-1)(3n-2)}$

Expressing summation as integral.

Show that the set $A$ contains an open interval.

Evaluate $\sum_{n=1}^\infty (-1)^{n+1}({1 - \cos(2n-1) \over 2n-1})$ using Fourier Series

Evaluate $\lim_{n\to \infty} \left( \sum_{r=0}^n \frac {2^r}{5^{2^r}+1}\right) $

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