x Turn on thread page Beta
 You are Here: Home >< Maths

# Simple silly binomial expansion question! watch

1. So I saw that the 2nd term of the sequence 1/(1-x) has is (-1)(-X)

But!!! I keep getting 1/2 seee n=-1 right and r=1 so n!/n(n-r)! =

n!= -1

r!(n-r)! = 1!((-1)-(1))! = 1!(-2!)= 2

so the 2nd term is -1/2 (-x)

Whyyyy it says everywhere that r!(n-r)! = r! whyyyyyyyyyyyyyyyyyyyyyy
2. Come on !!!!!!!! 21 views and not even one reply?
3. (Original post by Destroyviruses)
So I saw that the 2nd term of the sequence 1/(1-x) has is (-1)(-X)

But!!! I keep getting 1/2 seee n=-1 right and r=1 so n!/n(n-r)! =

n!= -1

r!(n-r)! = 1!((-1)-(1))! = 1!(-2!)= 2

so the 2nd term is -1/2 (-x)

Whyyyy it says everywhere that r!(n-r)! = r! whyyyyyyyyyyyyyyyyyyyyyy
You're approaching the expansion in the wrong way - As far as I know, the factorial of a negative number is undefined - think about what the definition of n! is (n.(n-1)!), and what that would mean for n < 0.

The binomial expansion of a function in the form 1/(1+ax) is:

It shouldn't be difficult to adjust the above and get the series you've seen with the second term "(-1)(-x)".

Hope that helped.
4. (Original post by EEngWillow)
You're approaching the expansion in the wrong way - As far as I know, the factorial of a negative number is undefined - think about what the definition of n! is (n.(n-1)!), and what that would mean for n < 0.

The binomial expansion of a function in the form 1/(1+ax) is:

It shouldn't be difficult to adjust the above and get the series you've seen with the second term "(-1)(-x)".

Hope that helped.
stil confused. I know how to use the equation but not how to derive it!!!! why isnt it r!(n-r)! instead of r! !!!!
5. (Original post by EEngWillow)
You're approaching the expansion in the wrong way - As far as I know, the factorial of a negative number is undefined - think about what the definition of n! is (n.(n-1)!), and what that would mean for n < 0.

The binomial expansion of a function in the form 1/(1+ax) is:

It shouldn't be difficult to adjust the above and get the series you've seen with the second term "(-1)(-x)".

Hope that helped.
Ohh are you sure its undefined? because the calculator doenst seem to think so
6. (Original post by Destroyviruses)
Ohh are you sure its undefined? because the calculator doenst seem to think so
If you type -1! into your calculator, it evaluates -(1!).

Try typing (-1)! instead, and you'll see it gives a math error.

8. (Original post by EEngWillow)
If you type -1! into your calculator, it evaluates -(1!).

Try typing (-1)! instead, and you'll see it gives a math error.
Ohhhh silly me. I just read the page on my math book properly and saw that

n(n-1)/r! etc

is an alternative one to the one I learnt!!! Silly me and my selective reading.

9. (Original post by noobynoo)

I got it, thanks for trying. I didn't realise there were two equations for this expansion business!
10. (Original post by EEngWillow)
You're approaching the expansion in the wrong way - As far as I know, the factorial of a negative number is undefined - think about what the definition of n! is (n.(n-1)!), and what that would mean for n < 0.

The binomial expansion of a function in the form 1/(1+ax) is:

It shouldn't be difficult to adjust the above and get the series you've seen with the second term "(-1)(-x)".

Hope that helped.
If I remember correctly you can using the gamma function -gamma(2)
11. (Original post by anshul95)
If I remember correctly you can using the gamma function -gamma(2)
Yes, you can, but gamma functions aren't in the A Level syllabus. (Or are they?!)
12. (Original post by EEngWillow)
Yes, you can, but gamma functions aren't in the A Level syllabus. (Or are they?!)
they aren't I was just telling you that you can.
13. (Original post by anshul95)
If I remember correctly you can using the gamma function -gamma(2)
What part are you suggesting using the gamma function for?
14. Well the formula is but for the first few terms they have used r = 1, 2, 3... etc.

So the the terms become:

.
15. (Original post by Farhan.Hanif93)
What part are you suggesting using the gamma function for?
I wasn't suggesting it be used in the question, but that EEngWillow said the factorial of a negative number was undefined. Which using the gamma function it isnt.
16. (Original post by anshul95)
I wasn't suggesting it be used in the question, but that EEngWillow said the factorial of a negative number was undefined. Which using the gamma function it isnt.
I'm afraid you're wrong there. The gamma function isn't defined for negative integers.
17. (Original post by Farhan.Hanif93)
I'm afraid you're wrong there. The gamma function isn't defined for negative integers.
ah yes you are right....just tried it on wolframalpha. You are just too sharp. I probably got carried away because you can do it for negative fractions. The correct answer looks quite cool though - complex infinity!!!

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: March 20, 2011
Today on TSR

### Boyfriend slept with someone else

...we were on a break

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams