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