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binomial expansion

Screen Shot 2019-05-05 at 14.07.39.png

why wouldn't the range of validity not be x<1/4

Original post by jeriu

Screen Shot 2019-05-05 at 14.07.39.png

why wouldn't the range of validity not be x<1/4

You don;t need a binomial expansion for that. (1 - 4x)(1 - 4x)(1 - 4x) ....

Study Forum Helper

Original post by jeriu

why wouldn't the range of validity not be x<1/4

Nope. It's valid for all

x

.

If it was

(1-4x)^{-3}

then the range of validity would be

|x| < \dfrac{1}{4}

.

(edited 4 years ago)

OP

Original post by RDKGames

Nope. It's valid for all

x

.

If it was

(1-4x)^{-3}

then the range of validity would be

|x| < \dfrac{1}{4}

.

why may i ask

Study Forum Helper

Original post by jeriu

why may i ask

(1-4x)^3

can be expressed as

1-12x + 48x^2 - 64x^3

. This is a finite sum for any

x

you put in, so it always converges onto a value.

(1-4x)^{-3}

cannot be expressed as a finite sum. It constitutes an infinite one, and with infinite sums, they converge only under certain conditions. For forms like these, this condition is precisely that we must have

x

as part of a certain interval.

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