Problem on #7 Ex12.11

: Math 2730 Sequences and Series: Problem on #7 Ex12.11
   By Ka Hei Stephanie Ng on Tuesday, April 22, 2008 - 05:39 am: Edit Post

The question is:
Use the binomial series to expand the function as a power series. State the radius of convergence.
x/root of(4+x^2)

I did it like this:
x/root of (4+x^2)
= x(1/2)[1+(x^2/4)]^(-1/2)
then i find the power series of [1+(x^2/4)]^(-1/2),and get:
sum of (from 0, infinity)[(-1)^n (3/2-n)(x^(2n))]/[n!4^n]

and then i multiply the power series by x(1/2)
and get:
sum of(from 0,infinity)[(-1)^n(3/2-n)(x^(2n+1))]/[n!2^(2n+1)]

which is different from the solution..Did i do anything wrong? I wonder if i can express the power series with fractions in it..


   By Sasho on Tuesday, April 22, 2008 - 08:03 am: Edit Post

Something is wrong with your solution; specifically, the term (3/2-n) is unclear. It seems to me that you have erred when you simplified the binomial coefficients.I suggest that you carefully do (1+x)-1/2 and then substitute x2/4 in place of x.


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