1. ## Radius and range of convergence

Hi, can someone please tell me what is the radius and range of convergence of sum(100^k*(x-1)^(2*k)/k, k = 1 .. infinity) ?

Any help would be greatly appreciated :-)

2. Originally Posted by Guardna
Hi, can someone please tell me what is the radius and range of convergence of sum(100^k*(x-1)^(2*k)/k, k = 1 .. infinity) ?

Any help would be greatly appreciated :-)
use the ratio test ...

$\lim_{k \to \infty} \left|\frac{a_{k+1}}{a_k} \right| < 1$

3. Originally Posted by skeeter
use the ratio test ...

$\lim_{k \to \infty} \left|\frac{a_{k+1}}{a_k} \right| < 1$

Thank you sir!

I was afraid of using the test of d'alembert because i thought k needed to start from 0 and not from 1.

4. root test is faster, try it.

5. It is indeed faster, thank you