Solved

1/(1-x)^k

Posted on 2013-05-24
5
156 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
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

Suggested Solutions

Title # Comments Views Activity
Q1. Magnets and Electromagnetism 33 124
Error in calculation 2 89
Independent Events 4 91
Dual bridge protection 18 156
Foreword (May 2015) This web page has appeared at Google.  It's definitely worth considering! https://www.google.com/about/careers/students/guide-to-technical-development.html How to Know You are Making a Difference at EE In August, 2013, one …
This article provides a brief introduction to tissue engineering, the process by which organs can be grown artificially. It covers the problems with organ transplants, the tissue engineering process, and the current successes and problems of the tec…
This is a video describing the growing solar energy use in Utah. This is a topic that greatly interests me and so I decided to produce a video about it.
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…

730 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