Expansion of a term with power 2/3

[quietrain]

Homework Statement

how am i suppose to expand

(X-4)^2/3

The Attempt at a Solution

i don't have any idea :(

any help?

thanks!

 

[quietrain]

oh i realize its bionomial expasion...

i never knew the power could be a fraction :X

 

[uart]

Yes the binomial expansion can be extended to non integer powers as :

$$(1 + x)^a = 1 + a x + a (a-1) \, \frac{x^2}{2!} + a (a-1)(a-2) \, \frac{x^3}{3!} + ...$$

This is an infinite series, but as you can easily see it terminates after a+1 terms (indeed to the regular binomial series) if "a" is a non-negative integer.

 

[quietrain]

oh i see thank you, but it doesn't terminate if a is a fraction right?

 

[uart]

oh i see thank you, but it doesn't terminate if a is a fraction right?

Yeah that's right, if "a" is anything other than a non-negative negative integer (that is, if its either negative or a fraction) then it's an infinite series.

It terminates for non-negative integers because eventually one of the terms in a(a-1)(a-2) ... goes to zero.

 

[quietrain]

i see thank you