List questions from binomial-theorem

Published on 21 Mar 2021 - 17:20

550

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Confusion on how extended binomial theorem works

Published on 23 Feb 2026 - 15:05

738

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Are binomial coefficients defined for $k \in \mathbb{R}$

Published on 23 Mar 2021 - 20:47

190

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Does the power rule come from the generalised binomial theorem or the other way around?

Published on 24 Mar 2021 - 4:45

137

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Upper bound for $\sum_{i = 0}^{k-1} {n \choose i} (1 - \varepsilon)^i\varepsilon^{n-i}$

Published on 03 Apr 2026 - 12:40

90

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Length of this expression can take in positive integers including 0

Published on 28 Mar 2021 - 6:59

173

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Solving $(z+i)^n+(z-i)^n=0$

Published on 30 Mar 2021 - 3:52

260

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How to find the coefficient of $x^2$ in $(3-2x) \left(1 + \frac{x}{2} \right)^n$

Published on 01 Apr 2021 - 4:25

285

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Use binomial series for $\sqrt{1+x}$ to find the binomial series for $\frac{1}{\sqrt{1+x}}$

Published on 01 Apr 2021 - 5:05

100

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Simplifying binomial series

Published on 30 Mar 2026 - 14:01

125

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Looking for formula for variation of binomial theorem

Published on 02 Apr 2021 - 23:22

631

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Calculating $ \sum_{k=0}{n\choose 4k+1}$

Published on 06 Apr 2021 - 20:41

1k

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'Binomial Expansion' - How to find value of term in expression with given coefficients?

Published on 08 Apr 2021 - 0:36

733

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Coefficient of $x^{12}$ in $(1+x^2+x^4+x^6)^n$

Published on 09 Apr 2021 - 15:02

159

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Combinatorial Summation

Published on 10 Apr 2021 - 14:38

List Question

$\sum_{m = 0}^n\binom{n}{2m}(-1)^m = 2^{\frac{n}{2}}\cos\left(\frac{n\pi}{4}\right)$

Confusion on how extended binomial theorem works

Are binomial coefficients defined for $k \in \mathbb{R}$

Does the power rule come from the generalised binomial theorem or the other way around?

Upper bound for $\sum_{i = 0}^{k-1} {n \choose i} (1 - \varepsilon)^i\varepsilon^{n-i}$

Length of this expression can take in positive integers including 0

Solving $(z+i)^n+(z-i)^n=0$

How to find the coefficient of $x^2$ in $(3-2x) \left(1 + \frac{x}{2} \right)^n$

Use binomial series for $\sqrt{1+x}$ to find the binomial series for $\frac{1}{\sqrt{1+x}}$

Simplifying binomial series

Looking for formula for variation of binomial theorem

Calculating $ \sum_{k=0}{n\choose 4k+1}$

'Binomial Expansion' - How to find value of term in expression with given coefficients?

Coefficient of $x^{12}$ in $(1+x^2+x^4+x^6)^n$

Combinatorial Summation

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