?(n=0 to inf)Cnx^n? Use the binomial series to expand the function f(x)=8x/sqrt(2+x) as a power series ?(n=0 to inf)Cnx^n
C0=?
C1=?
C2=?
C3=?
C4=?

You must use the generalized binomial series:

(2 + x)^(- 1/2) = ?[n = 0 to +?]C(- 1/2,n)2^((- 1/2) - n)(x^n) =

= (1/?2)?[n = 0 to +?]C(- 1/2,n)2^(- n)(x^n)

But:

C(- 1/2,n) = (1/n!)?[k = 0 to n - 1]((- 1/2) - n)

So:

f(x) = ?[n = 0 to +?]4?2C(- 1/2,n)2^(- n)(x^(n + 1))