List questions from binomial-theorem

Published on 25 May 2020 - 12:30

64

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How to show $\sum_{i=0}^{2m} (-1)^{i}\binom{2m}{i}^{2} = (-1)^m\binom{2m}{m}$

Published on 25 May 2020 - 16:00

105

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Reciprocal of square root of a binomial to series.

Published on 26 May 2020 - 6:11

127

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Evaluation of a tricky binomial sum

Published on 26 May 2020 - 20:55

65

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How can I show binomial series converges to $\sqrt {2}$?

Published on 30 May 2020 - 14:01

137

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How do I solve this problem using binomial theorem with square root in it?

Published on 31 May 2020 - 10:47

100

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Radius of convergence for binomial series (2)

Published on 01 Jun 2020 - 8:33

46

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calculate the given sum (related to Newton's binomial formula)

Published on 01 Jun 2020 - 12:15

45

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Closed for solution for $\sum_{k = 0}^{n} Q^{k} ( 1 - Q) ^ {k}$

Published on 01 Jun 2020 - 16:37

132

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Find the generating function and the number of integers solutions for $x_1 + x_2 + x_3 + x_4 = r$, where $-3 \leq x_i \leq 3$.

Published on 28 Mar 2026 - 7:27

114

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Evaluate the sum $\sum_{n=0}^{\infty} \frac{2n}{8^n}{{2n}\choose{n}}$

Published on 02 Jun 2020 - 18:44

112

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How may one solve problems over expressions like $(2+px)^6$ without the binomial theorem?

Published on 04 Jun 2020 - 3:37

187

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Combinations series: $\frac{{n \choose 1}(n-1)^3+{n \choose 3}(n-3)^3+\ldots}{n^2(n+3)\cdot 2^n}$

Published on 07 Jun 2020 - 16:32

51

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Does there exist integers $m,n$ satisfying a certain equation?

Published on 10 Jun 2020 - 5:01

129

Views

$2007^{201} + 2019^{201} - 1982^{201} - 2044^{201}$ is divisible by which of the following?

Published on 10 Jun 2020 - 6:50

List Question

Inverse of the difference of matrices

How to show $\sum_{i=0}^{2m} (-1)^{i}\binom{2m}{i}^{2} = (-1)^m\binom{2m}{m}$

Reciprocal of square root of a binomial to series.

Evaluation of a tricky binomial sum

How can I show binomial series converges to $\sqrt {2}$?

How do I solve this problem using binomial theorem with square root in it?

Radius of convergence for binomial series (2)

calculate the given sum (related to Newton's binomial formula)

Closed for solution for $\sum_{k = 0}^{n} Q^{k} ( 1 - Q) ^ {k}$

Find the generating function and the number of integers solutions for $x_1 + x_2 + x_3 + x_4 = r$, where $-3 \leq x_i \leq 3$.

Evaluate the sum $\sum_{n=0}^{\infty} \frac{2n}{8^n}{{2n}\choose{n}}$

How may one solve problems over expressions like $(2+px)^6$ without the binomial theorem?

Combinations series: $\frac{{n \choose 1}(n-1)^3+{n \choose 3}(n-3)^3+\ldots}{n^2(n+3)\cdot 2^n}$

Does there exist integers $m,n$ satisfying a certain equation?

$2007^{201} + 2019^{201} - 1982^{201} - 2044^{201}$ is divisible by which of the following?

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