Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

Partial fraction/binomial expansion question

I have a problem with understanding the point of the second part of the question. How to get an expansion of f(x) when it can go on forever? If I get an expression taking just till the coefficient of x^3 then it's a meaningless expression, and is incomplete?

you will get two separate expansions, one for each of the underneath brackets... select the terms in each up to x³ and combine them together.
as you say the whole expansion will be infinite but just keeping the low powers is very useful.

pleasedtobeatyou

If you are pedantic, put "..." after the expansions to indicate they continue

For example

(1-x)^-1[br][br]1 + x + x^2 + ...

Original post by bmqib

I have a problem with understanding the point of the second part of the question. How to get an expansion of f(x) when it can go on forever? If I get an expression taking just till the coefficient of x^3 then it's a meaningless expression, and is incomplete?

It is not meaningless

Since |x|<1 the higher powers of x are very small values

Therefore a small number of terms will give a good approximation

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