power series; 2
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Feb20-12, 10:46 PM
1. The problem statement, all variables and given/known data
Find the radius of convergence and interval of convergence of the series:
as n=1 to infinity: (n(x-4)^n) / (n^3 + 1)
2. Relevant equations
3. The attempt at a solution
i tried the ratio test but i ended up getting x had to be less than 25/4 ...
when i did it, i ended up with [ (n+1)(x-4)(n^3 + 1) ] / [(n+1)^3 + 1]
Perhaps it's just a typo, but you're missing a factor of
in the denominator.
take out the x-4 from the limit which leaves you with 4/9 * (x-4) and thats how i got it.
am i right or wrong? if so, how? not good at this stuff
You have the right idea, but I don't see where the 4/9 came from. Show us how you took the limit as n→∞.