Question

Prove that the circumference of an ellipse is given by this infinite series

score 558 · Answer 1 · 2026-03-29 08:57:55

558

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Prove that the circumference of an ellipse is given by this infinite series

Published on 29 Mar 2026 - 8:57

score 33 · Answer 2 · 2026-03-30 18:14:17

33

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How to write recursive relationship as a summation of matrices/vectors

Published on 30 Mar 2026 - 18:14

score 131 · Answer 3 · 2020-07-27 22:54:38

131

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Please explain how to do/calculate/read this Sigma notation?

Published on 27 Jul 2020 - 22:54

score 64 · Answer 4 · 2020-07-28 10:14:29

64

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How to find the number of terms in the expansion of $(a+b+c)^2$?

Published on 28 Jul 2020 - 10:14

score 114 · Answer 5 · 2020-07-28 10:46:41

114

Views

Simplifying $\sum_{k=0}^{24}\binom{100}{4k}.\binom{100}{4k+2}$

Published on 28 Jul 2020 - 10:46

score 58 · Answer 6 · 2020-07-28 14:31:54

58

Views

Sum of non-integer weighted binomial coefficients

Published on 28 Jul 2020 - 14:31

score 73 · Answer 7 · 2026-02-23 10:04:43

73

Views

Bounding coefficients of the polynomial $(1-x^2)^n (1-x)^{-m}$.

Published on 23 Feb 2026 - 10:04

score 89 · Answer 8 · 2026-03-27 13:44:36

89

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Prove $\sum_{b=0}^{n-1}b\binom{n+1-b}{2} = \binom{n+2}{4}$

Published on 27 Mar 2026 - 13:44

score 255 · Answer 9 · 2026-03-30 17:53:21

Prove that $\binom{n}{0}\binom{n+1}{n} +\binom{n}{1}\binom{n}{n-1} +\binom{n}{2}\binom{n-1}{n-2} +\cdots +\binom{n}{n}\binom{1}{0} = 2^{n-1}(n+2)$

score 90 · Answer 10 · 2026-03-30 17:53:21

If $y = \frac{2}{5}+\frac{1\cdot3}{2!} \left(\frac{2}{5}\right)^2+\frac{1\cdot3\cdot5}{3!} \left(\frac{2}{5}\right)^3+\cdots$, find $y^2+2y$

score 92 · Answer 11 · 2020-07-30 16:26:36

92

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$9$ Bags of coloured counters, $9$ grid squares. $3$ Counters can be laid at a time. How many permutations?

Published on 30 Jul 2020 - 16:26

score 231 · Answer 12 · 2026-04-09 02:59:08

231

Views

Monomials in terms of binomial coefficients

Published on 09 Apr 2026 - 2:59

score 1.7k · Answer 13 · 2016-07-07 15:11:04

1.7k

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How do you write a polynomial as a linear combination of binomial coefficients?

Published on 07 Jul 2016 - 15:11

score 4.3k · Answer 14 · 2016-07-08 06:01:58

4.3k

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Inverse of the Pascal Matrix

Published on 08 Jul 2016 - 6:01

score 67 · Answer 15 · 2016-07-08 14:09:39

67

Views

Compute this sum $\sum\limits_{i=3}^n \binom{n}{i} \frac{i!2^{i-3}}{(i-3)!}$

Published on 08 Jul 2016 - 14:09

List Question

Prove that the circumference of an ellipse is given by this infinite series

How to write recursive relationship as a summation of matrices/vectors

Please explain how to do/calculate/read this Sigma notation?

How to find the number of terms in the expansion of $(a+b+c)^2$?

Simplifying $\sum_{k=0}^{24}\binom{100}{4k}.\binom{100}{4k+2}$

Sum of non-integer weighted binomial coefficients

Bounding coefficients of the polynomial $(1-x^2)^n (1-x)^{-m}$.

Prove $\sum_{b=0}^{n-1}b\binom{n+1-b}{2} = \binom{n+2}{4}$

Prove that $\binom{n}{0}\binom{n+1}{n} +\binom{n}{1}\binom{n}{n-1} +\binom{n}{2}\binom{n-1}{n-2} +\cdots +\binom{n}{n}\binom{1}{0} = 2^{n-1}(n+2)$

If $y = \frac{2}{5}+\frac{1\cdot3}{2!} \left(\frac{2}{5}\right)^2+\frac{1\cdot3\cdot5}{3!} \left(\frac{2}{5}\right)^3+\cdots$, find $y^2+2y$

$9$ Bags of coloured counters, $9$ grid squares. $3$ Counters can be laid at a time. How many permutations?

Monomials in terms of binomial coefficients

How do you write a polynomial as a linear combination of binomial coefficients?

Inverse of the Pascal Matrix

Compute this sum $\sum\limits_{i=3}^n \binom{n}{i} \frac{i!2^{i-3}}{(i-3)!}$

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