Use differentiation and/or integration to express the following function as a power series (centered at x=0).

Question

Use differentiation and/or integration to express the following function as a power series (centered at x=0).

f(x)=1/((6+x)^3)

∞

f(x)=∑ _________

n=0

Answer 1

The nth derivative of 1/(6+x)^3 will be (-1)^n n+2!/2! (6+x)^-(3+n)

Thus, the Taylor series (recall the division by n!) is

n=∞

∑ (-1)^n(n+2)(n+1)/(2*6^(n+3))*x^n

n=0