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?