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## #1 2017-02-03 16:13:53

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,857
Website

### Sum with Binomial Coefficients

How do I simplify this?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #2 2017-02-03 16:16:25

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Sum with Binomial Coefficients

Did you try M?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #3 2017-02-03 17:39:12

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,857
Website

### Re: Sum with Binomial Coefficients

I did.

Here is a simplified version of that

$\mu^z \sum_{x=0}^{\color{blue}z}\binom z x(\frac\lambda\mu)^x~=~ \mu^z(1-\frac\lambda\mu)^z$

Last edited by Agnishom (2017-02-03 17:40:34)

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #4 2017-02-03 18:58:27

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Sum with Binomial Coefficients

Hmmm, why is that simpler?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #5 2017-02-04 16:31:28

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,857
Website

### Re: Sum with Binomial Coefficients

Don't you see that we can cancel the pair of mu^z in the numerator?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #6 2017-02-04 16:42:27

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Sum with Binomial Coefficients

Maybe for certain types of numbers you can make that simplification. There may be other types where you can not. You did not give any constraints on the constants. M warns us about automatically simplifying.

As you know humans say

M knows better and will not.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #7 2017-02-04 16:46:02

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,857
Website

### Re: Sum with Binomial Coefficients

Okay, I need to be able to deal with these Summations involving Binomial Coefficients without M's help

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #8 2017-02-04 16:47:20

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Sum with Binomial Coefficients

There is only one technique that I know of and jimmyR was an expert at it. I never did get the hang of it... It is called the snake oil method. To me asking this question

Okay, I need to be able to deal with these Summations involving Binomial Coefficients without M's help

is like asking I need to deal with problems like 1542366376371562524367477478484881424^19825634716 without M's help. Does not seem to make much sense...

Have you been following the Mathegocart combinatorics questions? I am defending EM rather well do you not think so?

How are you doing in school and in your life? Are you okay?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #9 2017-02-04 17:19:21

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,857
Website

### Re: Sum with Binomial Coefficients

It is not that bad, I need to tackle just some small subset of these problems by myself. They keep popping up in my probability theory course.

I have not seen Mathegocart's combinatorics problems. Where do I find them?

I am fine, I guess: I did laundry yesterday. Thanks for checking in. How are you doing?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #10 2017-02-04 17:53:27

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Sum with Binomial Coefficients

Hobbling around but still going.

Check out the snake oil method.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #11 2017-02-04 18:08:30

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,857
Website

### Re: Sum with Binomial Coefficients

In generatingfunctionology, right?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #12 2017-02-04 18:09:39

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Sum with Binomial Coefficients

I do not remember, it could be in A=B.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #13 2017-02-04 18:14:56

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,857
Website

### Re: Sum with Binomial Coefficients

Maybe, A = B has a lot of stuff about hypergeometric identities.

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #14 2017-02-04 18:16:44

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Sum with Binomial Coefficients

It is in my opinion and gAr's a very bad book.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #15 2017-02-05 03:12:26

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,857
Website

### Re: Sum with Binomial Coefficients

Whaaaaat? It is a book about experimental mathematics.

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #16 2017-02-05 05:00:06

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Sum with Binomial Coefficients

It is not written for us EM guys but appears to be written for those who would never do it!

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #17 2017-02-06 03:50:31

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,857
Website

### Re: Sum with Binomial Coefficients

Dolon Zeilberger is one of the co-authors.

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #18 2017-02-06 03:51:56

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Sum with Binomial Coefficients

Yes but I liked Herbert.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #19 2017-02-06 04:46:16

greg1313
Member
Registered: 2016-12-19
Posts: 17

### Re: Sum with Binomial Coefficients

bobbym wrote:

As you know humans say

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