# Edexcel C4 Binomial ExpansionWatch

#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.
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10 years ago
#2
Its because that can also be written as

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?
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#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?
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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.
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#5
Thank you. I understand that. But why does the series have to converge at all?
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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.
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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...
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#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.
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