Question

Any series which increases extremely slowly and whose lower bound is $\log^{\circ k}(n+1)$?

score 43 · Answer 1 · 2018-03-01 17:53:01

43

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Any series which increases extremely slowly and whose lower bound is $\log^{\circ k}(n+1)$?

Published on 01 Mar 2018 - 17:53

score 657 · Answer 2 · 2026-03-26 02:19:19

657

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Find a pattern and prove it by mathematical induction:

Published on 26 Mar 2026 - 2:19

score 7.6k · Answer 3 · 2026-03-25 02:37:17

7.6k

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Can we calculate $ i\sqrt { i\sqrt { i\sqrt { \cdots } } }$?

Published on 25 Mar 2026 - 2:37

score 70 · Answer 4 · 2026-03-25 17:39:44

70

Views

Proving $\sum_{k=0}^{p-1} {k \choose l}$ is divisible by p

Published on 25 Mar 2026 - 17:39

score 78 · Answer 5 · 2026-03-25 19:01:37

78

Views

Showing an identity between polynomials whose coefficients involve combinatorial identities

Published on 25 Mar 2026 - 19:01

score 74 · Answer 6 · 2026-03-17 15:52:44

74

Views

Does a sum require 2+ numbers, such as $sum(a, b, ...)$? Does $sum(n)$ imply $n + 0$?

Published on 17 Mar 2026 - 15:52

score 375 · Answer 7 · 2026-03-25 14:18:42

375

Views

Linear Mean Function

Published on 25 Mar 2026 - 14:18

score 92 · Answer 8 · 2026-03-26 07:35:34

92

Views

Prove the identity $ \sum\limits_{k=0}^{n-1} (-1)^{k} \binom{n}{k} (n-k) \frac{(a+k-2)!}{(a+k-n)!}=0.$

Published on 26 Mar 2026 - 7:35

score 13.4k · Answer 9 · 2018-03-03 11:36:16

13.4k

Views

How to interpret a sum with two indices?

Published on 03 Mar 2018 - 11:36

score 145 · Answer 10 · 2026-03-25 07:31:24

145

Views

Series involving product of Harmonic Numbers

Published on 25 Mar 2026 - 7:31

score 72 · Answer 11 · 2018-03-03 22:59:01

72

Views

How to calculate the summation of $w_i$, where $w_i = {n(n-1)\over (n-i)(i+1)}+{i-1\over i+1}w_{i-1}$

Published on 03 Mar 2018 - 22:59

score 99 · Answer 12 · 2026-03-25 22:09:20

99

Views

Summation Problem and finding its Modulus, how could I tackle it?

Published on 25 Mar 2026 - 22:09

score 529 · Answer 13 · 2026-03-26 07:34:47

529

Views

Infinite sum of a modified Bessel function of the first kind

Published on 26 Mar 2026 - 7:34

score 21 · Answer 14 · 2026-03-26 07:50:56

21

Views

proving the sum of a few determinant values as a constant

Published on 26 Mar 2026 - 7:50

score 211 · Answer 15 · 2026-03-22 19:00:43

211

Views

Is there finite number of $p$ such $\sum_{k=1}^{p-1}\left\{\frac{k^2}{p}\right\}=\frac{p-3}{2}？$

Published on 22 Mar 2026 - 19:00

List Question

Any series which increases extremely slowly and whose lower bound is $\log^{\circ k}(n+1)$?

Find a pattern and prove it by mathematical induction:

Can we calculate $ i\sqrt { i\sqrt { i\sqrt { \cdots } } }$?

Proving $\sum_{k=0}^{p-1} {k \choose l}$ is divisible by p

Showing an identity between polynomials whose coefficients involve combinatorial identities

Does a sum require 2+ numbers, such as $sum(a, b, ...)$? Does $sum(n)$ imply $n + 0$?

Linear Mean Function

Prove the identity $ \sum\limits_{k=0}^{n-1} (-1)^{k} \binom{n}{k} (n-k) \frac{(a+k-2)!}{(a+k-n)!}=0.$

How to interpret a sum with two indices?

Series involving product of Harmonic Numbers

How to calculate the summation of $w_i$, where $w_i = {n(n-1)\over (n-i)(i+1)}+{i-1\over i+1}w_{i-1}$

Summation Problem and finding its Modulus, how could I tackle it?

Infinite sum of a modified Bessel function of the first kind

proving the sum of a few determinant values as a constant

Is there finite number of $p$ such $\sum_{k=1}^{p-1}\left\{\frac{k^2}{p}\right\}=\frac{p-3}{2}？$

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