Find the interval of convergence for the given power series.
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Find the interval of convergence for the given power series.

[From: ] [author: ] [Date: 11-11-18] [Hit: ]
at x = 8 converges , x = 2 ,......
Find the interval of convergence for the given power series:
Sum[(x-5)^n / n(-3)^n] n=1 to infinity

My attempt thus far:
I think I need to do the ratio test?
lim[(x-5)^(n+1) / (n+1)(-3)^(n+1) * n(-3)^n / (x-5)^n] of n to infinity
simplify:
lim[(x-5)n / ((n+1)(-3)^(n+1))]
|x-5|*lim[n / -3(n+1)]
Do I need to try and move that -3 to outside the limit? How do I do that?
Then I tested the endpoints and got that they both converged, but that's assuming I did first part correctly, which I evidently didn't. Could someone please explain this to me? Thanks!

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1st : Ratio Test uses | a_(n+1) / a_n |...thus the ' - 3 ' is really + 3

2nd : lim {n--->∞ } = | x - 5} / 3 < 1---> ( 2 , 8 )..at x = 8 converges , x = 2 , diverges
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keywords: of,series,power,convergence,given,for,Find,the,interval,Find the interval of convergence for the given power series.
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