Edexcel C4 Binomial Expansion Watch

Snagglepuss
Badges: 7
Rep:
?
#1
Report Thread starter 10 years ago
#1
I don’t understand how to work out the range of values for x for which equations are valid. In the examples given, it seems to me the expansion is still valid if x has “non-valid” values.

Perhaps I am misunderstanding what is meant by “valid”. For example, on page 25 of the Heinemann book, Exercise 3A, Qu 1b, the expressions is:

1/(1- x)

And it’s valid only when |x|< 1.

Why is this, please? I appreciate that if x is greater than one, then the dominator is negative, but I don’t see why that is a problem.
0
quote
reply
clear.twilight
Badges: 0
Rep:
?
#2
Report 10 years ago
#2
Its because that can also be written as (1 - x)^{-1}

And if you have an expansion where the power is not a +ve integer (so -ve or a fraction) the expansion will not terminate and is only valid for -1 < x < 1, i.e. |x| < 1.

If you had for example (1 - 4x) to a power which was not a +ve integer the range of values it is valid for changes. in this case |-4x| < 1 i.e |x| < 1/4.

Does that help?
0
quote
reply
Snagglepuss
Badges: 7
Rep:
?
#3
Report Thread starter 10 years ago
#3
Many thanks ct. I understand what you say about the expansion not terminating, but I don't see why that matters. Why cannot one have values of x which leave the expansion infinite? What is wrong with that?
0
quote
reply
clear.twilight
Badges: 0
Rep:
?
#4
Report 10 years ago
#4
When your power is -ve or fractional the numerator will never contian (n - n) so the series will converge as long as |x| < 1.
0
quote
reply
Snagglepuss
Badges: 7
Rep:
?
#5
Report Thread starter 10 years ago
#5
Thank you. I understand that. But why does the series have to converge at all?
0
quote
reply
nota bene
Badges: 13
Rep:
?
#6
Report 10 years ago
#6
(Original post by Snagglepuss)
Thank you. I understand that. But why does the series have to converge at all?
The physicist's answer is: Because a divergent series is pretty useless to use to approximate something.
0
quote
reply
clear.twilight
Badges: 0
Rep:
?
#7
Report 10 years ago
#7
I'm trying to remember what my teacher said... I thinks its something to do with the formula... I think its because factorials are undefined for any numbers less than 0...
0
quote
reply
Snagglepuss
Badges: 7
Rep:
?
#8
Report Thread starter 10 years ago
#8
I am going to have some nice gin now, and will ponder this in the morning. Your point noted, NB, but I wasn't being asked to approximate anything. Just being too literal in my thought processes, perhaps, but then that is what we are suppsoed to be doing, I believe.

Gin will help. All will be clear.
0
quote
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

University open days

  • University of Lincoln
    Mini Open Day at the Brayford Campus Undergraduate
    Wed, 19 Dec '18
  • University of East Anglia
    UEA Mini Open Day Undergraduate
    Fri, 4 Jan '19
  • Bournemouth University
    Undergraduate Mini Open Day Undergraduate
    Wed, 9 Jan '19

Were you ever put in isolation at school?

Yes (282)
27.35%
No (749)
72.65%

Watched Threads

View All