## Math2400 one year ago Match each of the power series with its interval of convergence.

1. Math2400

Is this right? i only get one try so I wanted to be sure i got them ><

2. anonymous

Ill work them myself real quick to see

3. Math2400

aww thanks @Concentrationalizing i can post my work if that's easier

4. anonymous

I have better luck working it myself. Ive noticed that I can miss something a student does wrong if I just scan their work.

5. Math2400

haha sounds good :)

6. anonymous

1st one is fine.

7. Math2400

kk :)

8. anonymous

3 and 4 need to be flip-flopped

9. anonymous

Ill show the work

10. Math2400

kk thanks :)

11. Math2400

so it is C,B,D,A

12. Math2400

And if i could see ur work i'd appreciate that :)

13. anonymous

Via root test on #3 $\lim_{n \rightarrow \infty} \sqrt[n]{\left| \frac{ (x-9)^{n} }{ 9^{n} } \right|}$ $= \left| x-9 \right|\cdot \lim_{n \rightarrow \infty}\frac{ 1 }{ 9 } = \frac{ 1 }{ 9 }\left| x-9 \right|$ All the n's cancel and this is your limit. The conditions for root test are the same as for ratio test, we need to be less than 1. Thus we have: $\frac{ 1 }{ 9 }\left| x-9 \right| < 1 \implies \left| x-9 \right| < 9$ which would give you the (0,18) result (since its multiple choice, I assume we dont need to actually check the endpoints)

14. anonymous

i will not butt in and let @Concentrationalizing finish, but i am willing to bet you can guess at least two of these doing no work now i will go away

15. anonymous

Via ratio test on #4 $\lim_{n \rightarrow \infty}\left| \frac{ (x-9)^{n+1} }{ (n+1)!9^{n+1} }\cdot \frac{ 9^{n}n! }{ (x-9)^{n} } \right|$ $= \left| x-9 \right|\lim_{n \rightarrow\infty}\left| \frac{ 9^{n}n! }{ 9(n+1)9^{n}n! } \right|$ $= \left| x-9 \right|\lim_{n \rightarrow \infty}\left| \frac{ 1 }{ 9(n+1) } \right| = 0$ So all values of x work since we got a result of 0

16. anonymous

I could guess them, but I'm not comfortable enough doing that yet, I'd rather just do the work and make sure I'm correct, lol @satellite73 Anyway, normally these aren't multiple choice x_x

17. Math2400

haha thanks :)

18. anonymous

No problem :)