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Analytically: How does Pascal's triangle cook Sierpinski's triangle?

score 140 · Answer 1 · 2020-04-08 12:54:28

140

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Analytically: How does Pascal's triangle cook Sierpinski's triangle?

Published on 08 Apr 2020 - 12:54

score 84 · Answer 2 · 2026-03-24 15:04:03

84

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Proving an inequality involving real powers

Published on 24 Mar 2026 - 15:04

score 149 · Answer 3 · 2026-03-28 02:20:59

149

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Binomial expansion and combinatorics

Published on 28 Mar 2026 - 2:20

score 168 · Answer 4 · 2020-04-09 08:53:47

168

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A 'Difficult' Binomial Sum - Variable Base and Exponent

Published on 09 Apr 2020 - 8:53

score 169 · Answer 5 · 2020-04-09 12:57:13

169

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Find $r$ which maximizes $\binom{20}r\binom{20}0+\binom{20}{r-1}\binom{20}1+\binom{20}{r-2}\binom{20}2+\cdots+\binom{20}0\binom{20}r$

Published on 09 Apr 2020 - 12:57

score 107 · Answer 6 · 2020-04-12 19:51:17

107

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Binomial Series and the nth derivative

Published on 12 Apr 2020 - 19:51

score 51 · Answer 7 · 2020-04-14 12:56:57

51

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A proof of Bernouilli's inequality

Published on 14 Apr 2020 - 12:56

score 44 · Answer 8 · 2020-04-15 20:56:40

44

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$\sum \limits_{x=k}^{\infty}~ {x-1 \choose k-1}~ q^{x-k}~z^x = z^k(1-qz)^{-k} $

Published on 15 Apr 2020 - 20:56

score 287 · Answer 9 · 2026-03-26 17:52:50

287

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Raising a continued fraction to a power

Published on 26 Mar 2026 - 17:52

score 437 · Answer 10 · 2026-03-27 02:36:09

437

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Is there an expression for the coefficients of the falling factorial $x^{\underline n} \equiv x (x-1) \dots (x-n+1)$?

Published on 27 Mar 2026 - 2:36

score 146 · Answer 11 · 2020-04-17 20:09:29

146

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Evaluating $\sum_{r=1}^{3n-1}\dfrac{(-1)^{r-1}\cdot r}{\binom{3n}r}$

Published on 17 Apr 2020 - 20:09

score 58 · Answer 12 · 2020-04-21 21:28:32

58

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Binomial Theorem / Taylor Series Help

Published on 21 Apr 2020 - 21:28

score 43 · Answer 13 · 2026-03-28 03:55:34

43

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Using binomial distribution, how can I find tthe probability of getting <= 3 fives in 20 rolls of a dice?

Published on 28 Mar 2026 - 3:55

score 84 · Answer 14 · 2020-04-22 20:57:29

84

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Evaluate $\frac{\binom{n}{0}}{m!}+n\cdot\frac{\binom{n}{1}}{(m+1)!}+n(n-1)\cdot\frac{\binom{n}{2}}{(m+2)!}+\ldots$

Published on 22 Apr 2020 - 20:57

score 135 · Answer 15 · 2020-04-23 19:11:00

135

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Find coefficients of $x^2$ and $x^3$ in the expansion of $(3 − 2x) ^6$

Published on 23 Apr 2020 - 19:11

List Question

Analytically: How does Pascal's triangle cook Sierpinski's triangle?

Proving an inequality involving real powers

Binomial expansion and combinatorics

A 'Difficult' Binomial Sum - Variable Base and Exponent

Find $r$ which maximizes $\binom{20}r\binom{20}0+\binom{20}{r-1}\binom{20}1+\binom{20}{r-2}\binom{20}2+\cdots+\binom{20}0\binom{20}r$

Binomial Series and the nth derivative

A proof of Bernouilli's inequality

$\sum \limits_{x=k}^{\infty}~ {x-1 \choose k-1}~ q^{x-k}~z^x = z^k(1-qz)^{-k} $

Raising a continued fraction to a power

Is there an expression for the coefficients of the falling factorial $x^{\underline n} \equiv x (x-1) \dots (x-n+1)$?

Evaluating $\sum_{r=1}^{3n-1}\dfrac{(-1)^{r-1}\cdot r}{\binom{3n}r}$

Binomial Theorem / Taylor Series Help

Using binomial distribution, how can I find tthe probability of getting <= 3 fives in 20 rolls of a dice?

Evaluate $\frac{\binom{n}{0}}{m!}+n\cdot\frac{\binom{n}{1}}{(m+1)!}+n(n-1)\cdot\frac{\binom{n}{2}}{(m+2)!}+\ldots$

Find coefficients of $x^2$ and $x^3$ in the expansion of $(3 − 2x) ^6$

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