1. ## Power Series Question

Question: What is the radius of convergence for the power series: $\displaystyle$\displaystyle\sum\limits_{n=0}^\infty \sqrt{n(n+1)}(\pi t+7)^{n}

I am totally not sure about how to solve this question. I have learned techniques of ratio test and also root test. I need a jump start!

Thanks.

2. $\displaystyle \displaystyle r=\lim_{n\to\infty}\left|\frac{c_n}{c_{n+1}}\right |$

3. Does the n = 0 make a difference since usually the questions have n = 1. Also for the ratio test since it $\displaystyle \displaystyle r=\lim_{n\to\infty}\left|\frac{c_{n+1}}{c_{n}}\rig ht|$

4. Just run the limit as it is shown.

5. So which formula is correct? The one you showed or the one i replied with?

6. You are correct. Sorry about that.

7. Ok, i'll give that a try then!

8. I got $\displaystyle L = |\pi t +7|$, so since we want to have series convergence, $\displaystyle R = 1$?

Since, $\displaystyle |\pi t +7| < 1$ series converges and $\displaystyle |\pi t +7| > 1$, series diverges?