How do I calculate for the power serie $\sum_{k=1}^{\infty}\frac{1}{k2^k}z^k$ the development point $z_0\in \mathbb{C}$ and convergence radius?

Question

How do I calculate for the power serie $\sum_{k=1}^{\infty}\frac{1}{k2^k}z^k$ the development point $z_0\in \mathbb{C}$ and convergence radius $R\in \left [ 0,\infty \right ]$?

What is the definition of "the development point" in connection with a power series? I've heard of a power series expansion centered at a point $z_0$, but I'm not familiar with the term you are using. — hardmath, Apr 11 '17 at 02:11

score 2 · Accepted Answer · answered Apr 10 '17 at 19:49

2

1) This is a series in powers of $z = z - 0$, so $z_0 = 0$.

2) Use the Ratio Test.

answered Apr 10 '17 at 19:49

Robert Israel

448,999

How do I calculate for the power serie $\sum_{k=1}^{\infty}\frac{1}{k2^k}z^k$ the development point $z_0\in \mathbb{C}$ and convergence radius?

1 Answers1