Originally Posted by

**Arron** I just need to verify my answer to the following problem

Use the General Bionomial Theorem to determine first four terms of the Taylor series at 0 for the function

f(x) = (1-2x)^-1/3

I have

By the General Bionomial Theorem

(1-2x)^-1/3

(-1/3)

( n ) x^n, for |x|<1

Where

(-1/3)

( n ) = (-1/3)(-4/3)(-7/3)....(-1/3-n=1) / n!

hence

(1-2x)^-1/3

= 1 + (-1/3)/1 -2x + (-1/3)(-4/3)/2! -2x^2 + (-1/3)(-4/3)(-7/3)/3! -2x^3 .....

= 1+ 2/3x - 4/9x^2 + 28/81x^3 ........

I also need to state the radius of convergence of this power series.

can anyone help?