Solved

1/(1-x)^k

Posted on 2013-05-24
5
157 Views
Last Modified: 2013-07-20
I didn't understand the circled part in the attached photo ?

Is it binomial ? However, -k may be negative and there is no negative number in binomial theory ?
question.png
0
Comment
Question by:codeBuilder
[X]
Welcome to Experts Exchange

Add your voice to the tech community where 5M+ people just like you are talking about what matters.

  • Help others & share knowledge
  • Earn cash & points
  • Learn & ask questions
5 Comments
 
LVL 24

Expert Comment

by:aadih
ID: 39195760
0
 
LVL 15

Expert Comment

by:ChloesDad
ID: 39195777
yes it is binomial, k is a positive integer.

Wiki has some information about negative binomials

http://en.wikipedia.org/wiki/Binomial_coefficient
0
 
LVL 31

Expert Comment

by:GwynforWeb
ID: 39195827
if Bin(k,n) = k!/(n!(k-n)!

then

Bin(-k,n) =(-1)^n *k!/(n!(k-n)!

               = (-1)^n *Bin(k,n)

So for instance  

  1/(1-x) = 1+ x + x² + x³ + ....

To really understand why this is the case requires going beyond Pascal's triangle. These ideas are often presented without sufficient justification, in essence they are saying:- believe me it is true and it works.

The coefficients for -ve and fractional powers come from looking at the problem as a Taylor Series expansion.
0
 

Author Comment

by:codeBuilder
ID: 39195884
Bin(k,n) = k!/(n!(k-n)!
Bin(-k,n) =(-1)^n *k!/(n!(k-n)!


Each has one paranthesis which don't have any mathcing paranthesis?
Can you fix it please @GwynforWeb ?
0
 
LVL 31

Accepted Solution

by:
GwynforWeb earned 500 total points
ID: 39196035
Sorry it is this

Bin(k,n) = k!/(n!(k-n)!)
Bin(-k,n) =(-1)^n *k!/(n!(k-n)!)
0

Featured Post

Technology Partners: We Want Your Opinion!

We value your feedback.

Take our survey and automatically be enter to win anyone of the following:
Yeti Cooler, Amazon eGift Card, and Movie eGift Card!

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

Have you ever thought of installing a power system that generates solar electricity to power your house? Some may say yes, while others may tell me no. But have you noticed that people around you are now considering installing such systems in their …
When we purchase storage, we typically are advertised storage of 500GB, 1TB, 2TB and so on. However, when you actually install it into your computer, your 500GB HDD will actually show up as 465GB. Why? It has to do with the way people and computers…
Although Jacob Bernoulli (1654-1705) has been credited as the creator of "Binomial Distribution Table", Gottfried Leibniz (1646-1716) did his dissertation on the subject in 1666; Leibniz you may recall is the co-inventor of "Calculus" and beat Isaac…
Finds all prime numbers in a range requested and places them in a public primes() array. I've demostrated a template size of 30 (2 * 3 * 5) but larger templates can be built such 210  (2 * 3 * 5 * 7) or 2310  (2 * 3 * 5 * 7 * 11). The larger templa…

695 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.

Join & Ask a Question