Question

simplifying triple summations from series expansion

score 96 · Answer 1 · 2026-03-26 06:19:18

96

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simplifying triple summations from series expansion

Published on 26 Mar 2026 - 6:19

score 112 · Answer 2 · 2018-08-25 04:54:41

112

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

Published on 25 Aug 2018 - 4:54

score 604 · Answer 3 · 2018-08-25 23:40:52

604

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Binomial expansion lower bound $A^n + B^n \le (A+B)^n$ for non-integer $n$

Published on 25 Aug 2018 - 23:40

score 38 · Answer 4 · 2018-08-27 10:50:48

38

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When proving $\binom{n}{r} = \binom{n-1}{r} + \binom{n-1}{r-1}$ per induction over $n$, why don’t we need induction over $r$?

Published on 27 Aug 2018 - 10:50

score 513 · Answer 5 · 2018-09-01 07:55:34

513

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Expand $\sqrt{1-x}$ up to and including the term $x^2$ (How should i proceed further)

Published on 01 Sep 2018 - 7:55

score 333 · Answer 6 · 2026-03-25 14:25:26

333

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Express $\frac x{x^2-3x + 2}$ in the partial fraction form and show that its partial fraction $x^3$ can be neglected

Published on 25 Mar 2026 - 14:25

score 72 · Answer 7 · 2018-09-02 11:10:46

72

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Prove that $3^{16} -33$ and $3^{15} +5$ is divisible by 4 by means of binomial theorem

Published on 02 Sep 2018 - 11:10

score 88 · Answer 8 · 2018-09-04 12:48:57

88

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$\sum_{k=0}^n \binom{n}{k}x^k(1-x)^{n-k}k$?

Published on 04 Sep 2018 - 12:48

score 70 · Answer 9 · 2018-09-09 06:58:44

70

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Expansion of $(\frac{x+2}{x})^{-\frac{1}{2}}$ and then find an approximate value...

Published on 09 Sep 2018 - 6:58

score 101 · Answer 10 · 2018-09-13 18:23:15

101

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Find the coefficient of a negative indexed $x$ in a series expansion

Published on 13 Sep 2018 - 18:23

score 1.5k · Answer 11 · 2026-03-25 19:12:06

1.5k

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I don't see how the binomial theorem relates to the principle of inclusion and exclusion?

Published on 25 Mar 2026 - 19:12

score 51 · Answer 12 · 2018-09-14 09:30:15

51

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The number of ways in which n identical items can be divided into r groups so that no group contain less than m items and more than k$(m<k)$ is

Published on 14 Sep 2018 - 9:30

score 181 · Answer 13 · 2018-09-14 16:29:39

181

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If there are m items of one kind,n items of another kind and so on, then the number of ways of choosing r items of these items is

Published on 14 Sep 2018 - 16:29

score 137 · Answer 14 · 2018-09-15 06:32:31

137

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Find the number of 5-member committees which include at least two Republicans

Published on 15 Sep 2018 - 6:32

score 152 · Answer 15 · 2018-09-16 05:08:00

152

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Greatest term of this expansion?

Published on 16 Sep 2018 - 5:08

List Question

simplifying triple summations from series expansion

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

Binomial expansion lower bound $A^n + B^n \le (A+B)^n$ for non-integer $n$

When proving $\binom{n}{r} = \binom{n-1}{r} + \binom{n-1}{r-1}$ per induction over $n$, why don’t we need induction over $r$?

Expand $\sqrt{1-x}$ up to and including the term $x^2$ (How should i proceed further)

Express $\frac x{x^2-3x + 2}$ in the partial fraction form and show that its partial fraction $x^3$ can be neglected

Prove that $3^{16} -33$ and $3^{15} +5$ is divisible by 4 by means of binomial theorem

$\sum_{k=0}^n \binom{n}{k}x^k(1-x)^{n-k}k$?

Expansion of $(\frac{x+2}{x})^{-\frac{1}{2}}$ and then find an approximate value...

Find the coefficient of a negative indexed $x$ in a series expansion

I don't see how the binomial theorem relates to the principle of inclusion and exclusion?

The number of ways in which n identical items can be divided into r groups so that no group contain less than m items and more than k$(m<k)$ is

If there are m items of one kind,n items of another kind and so on, then the number of ways of choosing r items of these items is

Find the number of 5-member committees which include at least two Republicans

Greatest term of this expansion?

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