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C4 binomial expansion help

hey guys a quick question
I ve noticed something strange on the mark schemes about the set of values of x for which the expansion is valid.
in the book it says mod x < 1. but in some mark schemes it says mod x < or =1. which one is right and what is the difference? thanks a lot.
Reply 1
Avatar for Nirgilis
Nirgilis
14
Moved to Maths Help :h: . They're probably better placed to help you :yep:
Reply 2
Avatar for davros
davros
16
Original post by physicsftw
hey guys a quick question
I ve noticed something strange on the mark schemes about the set of values of x for which the expansion is valid.
in the book it says mod x < 1. but in some mark schemes it says mod x < or =1. which one is right and what is the difference? thanks a lot.


I would expect the inequality to be strictly less than.

Do you have an example of a question and mark scheme where they use "<="?
Reply 3
Avatar for physicsftw
physicsftw
OP
hm i think it's ocr mei c4 either june 2012 or jan 2012 but it was definitely <=
Reply 4
Avatar for davros
davros
16
Original post by physicsftw
hm i think it's ocr mei c4 either june 2012 or jan 2012 but it was definitely <=


Are you thinking of June 2012 Q2 by any chance? I've just found an old pdf with the mark scheme in it!

The main mark scheme states quite clearly that |x| < 1/2 was the expected answer. However, there is a side note that the expansion is actually correct for |x| <= 1/2 in this case, so they would have accepted that answer.
Reply 5
Avatar for physicsftw
physicsftw
OP
thanks. But i was jus wondering whats the difference
Reply 6
Avatar for davros
davros
16
Original post by physicsftw
thanks. But i was jus wondering whats the difference


Every power series, i.e. a series of the form

Σanzn\Sigma a_nz^n

has what's called a Radius of Convergence R, and the series converges for every z with |z| < R.

However, the tests that tell you the value of R don't guarantee what happens when z = R or z = -R - you usually have to treat those cases separately.

So as far as the A level binomial series is concerned, you should always write |x| < something. It might be that the series converges as well when x = something or x = -something, but you won't be expected to know that or check it at A level!
Reply 7
Avatar for physicsftw
physicsftw
OP
Original post by davros
Every power series, i.e. a series of the form

Σanzn\Sigma a_nz^n

has what's called a Radius of Convergence R, and the series converges for every z with |z| < R.

However, the tests that tell you the value of R don't guarantee what happens when z = R or z = -R - you usually have to treat those cases separately.

So as far as the A level binomial series is concerned, you should always write |x| < something. It might be that the series converges as well when x = something or x = -something, but you won't be expected to know that or check it at A level!

got it thanks

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