[Math] use differentiation to find a power series representation for 1/(3+x)^2

Question

would anyone tell me how to solve this?

Use differentiation to find a power series representation for

$$\frac{1}{(3+x)^{2}}$$

What is the radius of convergence, R?

Answer 1

Possible hint: We have $$1/(3 + x)=(1/3)\frac{1}{(1-(-x/3))}$$ Use this fact that $1/(1-t)=\sum_0^{\infty}t^n~~~(*)$ where $|t|<1$. I mean take $t=-x/3$ and...

Note that $|-t|=|t|<1$ is the radius of convergence of $(*)$