Question

Understanding why binomial expansions for negative integers produce infinite series

score 1.5k · Answer 1 · 2020-09-02 07:43:36

1.5k

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Understanding why binomial expansions for negative integers produce infinite series

Published on 02 Sep 2020 - 7:43

score 695 · Answer 2 · 2020-09-03 04:13:26

695

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Notation for binomial expansion of sum of 2 matrices

Published on 03 Sep 2020 - 4:13

score 60 · Answer 3 · 2020-09-03 11:33:45

60

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How to prove that $\sum_{k=0}^{\infty} \frac{1}{1+k} {9/2 \choose k}=\frac{2}{11}~(32\sqrt{2}-1)$

Published on 03 Sep 2020 - 11:33

score 153 · Answer 4 · 2026-03-26 04:34:28

153

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Methods to find coefficient of a term in sum of polynomials

Published on 26 Mar 2026 - 4:34

score 57 · Answer 5 · 2020-09-05 02:53:37

57

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Cubic numbers that can be divided by $2^{26} \cdot 3^{16} \cdot 5^8 \cdot 7^4$

Published on 05 Sep 2020 - 2:53

score 67 · Answer 6 · 2020-09-05 05:25:16

67

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Let $S_p=\sum_{k=0}^{\infty} {-p \choose k} (1+k)^{-p}$, how to show that $S_1=S_2=\ln 2$

Published on 05 Sep 2020 - 5:25

score 98 · Answer 7 · 2020-09-05 18:53:26

98

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Explicitly evaluating powers of a sum of non-commuting matrices

Published on 05 Sep 2020 - 18:53

score 229 · Answer 8 · 2026-04-02 10:42:15

229

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Convergence of the sum of products $\sum_{k=0}^\infty \prod_{j=1}^k \left(1-\frac{3}{2j}\right)$

Published on 02 Apr 2026 - 10:42

score 126 · Answer 9 · 2020-09-08 15:11:13

126

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Evaluate:${30 \choose 0}{20 \choose 10}+{31 \choose 1}{19 \choose 10}+{32 \choose 2}{18 \choose 10}+\ldots +{40 \choose 10}{10 \choose 10}$

Published on 08 Sep 2020 - 15:11

score 149 · Answer 10 · 2020-09-09 09:08:28

149

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Why do binomial expansions involving surds get closer to integers as they get larger?

Published on 09 Sep 2020 - 9:08

score 51 · Answer 11 · 2020-09-10 11:26:59

51

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Divisibility of higher power polynomials

Published on 10 Sep 2020 - 11:26

score 63 · Answer 12 · 2020-09-13 17:12:57

63

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Binomial Theorem Derivative Identity

Published on 13 Sep 2020 - 17:12

score 56 · Answer 13 · 2026-02-23 15:06:45

56

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Sum of binomial numbers alternating the sign.

Published on 23 Feb 2026 - 15:06

score 41 · Answer 14 · 2026-02-23 15:06:45

41

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Sum of binomial numbers alternating the sign with complexes.

Published on 23 Feb 2026 - 15:06

score 104 · Answer 15 · 2026-03-30 00:21:21

104

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Combinatorial Proof for $\binom{n}{k}-\binom{n-3}{k} = \binom{n-1}{k-1} + \binom{n-2}{k-1} + \binom{n-3}{k-1}$

Published on 30 Mar 2026 - 0:21

List Question

Understanding why binomial expansions for negative integers produce infinite series

Notation for binomial expansion of sum of 2 matrices

How to prove that $\sum_{k=0}^{\infty} \frac{1}{1+k} {9/2 \choose k}=\frac{2}{11}~(32\sqrt{2}-1)$

Methods to find coefficient of a term in sum of polynomials

Cubic numbers that can be divided by $2^{26} \cdot 3^{16} \cdot 5^8 \cdot 7^4$

Let $S_p=\sum_{k=0}^{\infty} {-p \choose k} (1+k)^{-p}$, how to show that $S_1=S_2=\ln 2$

Explicitly evaluating powers of a sum of non-commuting matrices

Convergence of the sum of products $\sum_{k=0}^\infty \prod_{j=1}^k \left(1-\frac{3}{2j}\right)$

Evaluate:${30 \choose 0}{20 \choose 10}+{31 \choose 1}{19 \choose 10}+{32 \choose 2}{18 \choose 10}+\ldots +{40 \choose 10}{10 \choose 10}$

Why do binomial expansions involving surds get closer to integers as they get larger?

Divisibility of higher power polynomials

Binomial Theorem Derivative Identity

Sum of binomial numbers alternating the sign.

Sum of binomial numbers alternating the sign with complexes.

Combinatorial Proof for $\binom{n}{k}-\binom{n-3}{k} = \binom{n-1}{k-1} + \binom{n-2}{k-1} + \binom{n-3}{k-1}$

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