Question

Function maximized by $\left\{\left\lfloor\frac np\right\rfloor,\dots,\left\lfloor\frac{n+p-j}p\right\rfloor\right\}$

score 177 · Answer 1 · 2022-01-03 15:02:54

177

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Function maximized by $\left\{\left\lfloor\frac np\right\rfloor,\dots,\left\lfloor\frac{n+p-j}p\right\rfloor\right\}$

Published on 03 Jan 2022 - 15:02

score 80 · Answer 2 · 2022-01-06 21:35:14

80

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What does this Adjusted Binomial Expansion approach for one half?

Published on 06 Jan 2022 - 21:35

score 761 · Answer 3 · 2022-01-07 10:18:27

761

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Finding the term independent of $x$ in $\left(e^x+e^{-x}+\ln e^{x+2}\right)^{20}$.

Published on 07 Jan 2022 - 10:18

score 55 · Answer 4 · 2022-01-11 03:56:42

55

Views

If particular terms of a binomial expansion are given then does it need to be a unique expansion?

Published on 11 Jan 2022 - 3:56

score 37 · Answer 5 · 2022-01-12 13:46:55

37

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Is the series expansion of $\frac1{(1+x)^n}$ same as $\frac1{(1-x)^n}$ with $(-1)^r$

Published on 12 Jan 2022 - 13:46

score 38 · Answer 6 · 2022-01-16 03:09:24

38

Views

Evaluating $ \binom{n}{0} + 2 \binom{n}{1} + 2^2 \binom{n}{2} + \dots + 2^k \binom{n}{k} + \dots + 2^n \binom{n}{n} $

Published on 16 Jan 2022 - 3:09

score 172 · Answer 7 · 2022-01-18 22:36:58

172

Views

Can we re-write Newton's Binomial formula as a power series in $\ r\ $ without any problems?

Published on 18 Jan 2022 - 22:36

score 68 · Answer 8 · 2022-01-28 14:17:13

68

Views

Elementary number theory problem involving binomial theorem

Published on 28 Jan 2022 - 14:17

score 276 · Answer 9 · 2022-02-01 05:39:31

276

Views

Given that $z=1+i$, find the value of $n\in\mathbb{Z^+}$ such that $z^n$ is real.

Published on 01 Feb 2022 - 5:39

score 58 · Answer 10 · 2022-02-01 19:29:16

58

Views

Prove that $(\frac{13}{16})^{12}=\sum_{k=0}^{12}{12 \choose k}\left(\frac{1}{4}\right)^{2k}\left(\frac{3}{4}\right)^{12-k}$

Published on 01 Feb 2022 - 19:29

score 83 · Answer 11 · 2022-02-03 21:03:17

83

Views

Proving divisibility by induction

Published on 03 Feb 2022 - 21:03

score 199 · Answer 12 · 2022-02-04 16:57:53

199

Views

Binomial expansion of $(1+x)^i$ where $i^2 = -1$.

Published on 04 Feb 2022 - 16:57

score 121 · Answer 13 · 2022-02-04 21:26:44

121

Views

Show that $\sum_{i=0}^{n}\binom{k}{i}=2^{k-1}$

Published on 04 Feb 2022 - 21:26

score 132 · Answer 14 · 2022-02-10 17:20:13

132

Views

Given $P_n(x)=\frac1{2^n}\left[(x+\sqrt{x^2-1})^n+(x-\sqrt{x^2-1})^n\right]$, prove $P_n(x)-xP_{n-1}(x)+\frac{1}{4}P_{n-2}(x)=0$

Published on 10 Feb 2022 - 17:20

score 87 · Answer 15 · 2022-02-13 12:46:50

87

Views

Aymptotic formula/closed form for $ \sum_{r=1}^{n} {n \choose r} \frac{f^{(r-1)}(1)}{(r-1)!}$

Published on 13 Feb 2022 - 12:46

List Question

Function maximized by $\left\{\left\lfloor\frac np\right\rfloor,\dots,\left\lfloor\frac{n+p-j}p\right\rfloor\right\}$

What does this Adjusted Binomial Expansion approach for one half?

Finding the term independent of $x$ in $\left(e^x+e^{-x}+\ln e^{x+2}\right)^{20}$.

If particular terms of a binomial expansion are given then does it need to be a unique expansion?

Is the series expansion of $\frac1{(1+x)^n}$ same as $\frac1{(1-x)^n}$ with $(-1)^r$

Evaluating $ \binom{n}{0} + 2 \binom{n}{1} + 2^2 \binom{n}{2} + \dots + 2^k \binom{n}{k} + \dots + 2^n \binom{n}{n} $

Can we re-write Newton's Binomial formula as a power series in $\ r\ $ without any problems?

Elementary number theory problem involving binomial theorem

Given that $z=1+i$, find the value of $n\in\mathbb{Z^+}$ such that $z^n$ is real.

Prove that $(\frac{13}{16})^{12}=\sum_{k=0}^{12}{12 \choose k}\left(\frac{1}{4}\right)^{2k}\left(\frac{3}{4}\right)^{12-k}$

Proving divisibility by induction

Binomial expansion of $(1+x)^i$ where $i^2 = -1$.

Show that $\sum_{i=0}^{n}\binom{k}{i}=2^{k-1}$

Given $P_n(x)=\frac1{2^n}\left[(x+\sqrt{x^2-1})^n+(x-\sqrt{x^2-1})^n\right]$, prove $P_n(x)-xP_{n-1}(x)+\frac{1}{4}P_{n-2}(x)=0$

Aymptotic formula/closed form for $ \sum_{r=1}^{n} {n \choose r} \frac{f^{(r-1)}(1)}{(r-1)!}$

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