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# C4 Binomial expansion - values for which expansions are valid? watch

1. My textbook goes on about finding the values for which the expansion is valid, usually mod x < 1, but I have no idea how to get it or what it means... Could anyone explain what it means and how do I find it out for a particular expansion?

For example, (1-x)^1/3

How would you know what values it is valid for?
2. (Original post by lollage123)
My textbook goes on about finding the values for which the expansion is valid, usually mod x < 1, but I have no idea how to get it or what it means... Could anyone explain what it means and how do I find it out for a particular expansion?

For example, (1-x)^1/3

How would you know what values it is valid for?
Take: Here the is the "" for which
So:
?
3. (Original post by lollage123)
My textbook goes on about finding the values for which the expansion is valid, usually mod x < 1, but I have no idea how to get it or what it means... Could anyone explain what it means and how do I find it out for a particular expansion?

For example, (1-x)^1/3

How would you know what values it is valid for?
The reason is that the series for (1+x)^n goes like:

If mod x >= 1, it's clear that this will never converge because x^2 > x, x^3 > x^2, …
But if mod x < 1, it has a chance of converging because x^2 < x, etc - the terms are getting smaller. It can be shown rigorously that indeed the series converges for mod x < 1 (but that's a big kettle of fish involving analysis and the ratio test).

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