- #1
xspook
- 19
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Homework Statement
Determine the radius of convergence and the interval of convergence og the folling power series:
n=0 to infinity
Ʃ=[itex]\frac{(2x-3)^{n}}{ln(2n+3)}[/itex]
Homework Equations
Ratio Test
The Attempt at a Solution
Well I started with the ratio test but I have no clue where to go with it
[itex]\frac{(2x-3)^{n+1}}{ln(2(n+1)+3)}[/itex] * [itex]\frac{ln(2n+3)}{(2x-3)^{n}}[/itex]
I know that I will be left with the 2x-3 and I can pull that out in front of the limit to use when doing the interval of convergence, but I am lost with the natural log. should I distribute the two and make it
[itex]\frac{(2x-3)^{n+1}}{ln(2n+5)}[/itex] * [itex]\frac{ln(2n+3)}{(2x-3)^{n}}[/itex]
2x-3 Lim as n approaches infinity of : ln(2n+3)-ln(2n+5)??
Any help would be appreciated