Radius of Convergence

  • #1
ReidMerrill
68
2

Homework Statement


Find all values of x such that the given series would converge

Σ6n(x-5)n(n+1)/(n+11)

Homework Equations




The Attempt at a Solution


By doing the ratio test I found that
lim 6n(x-5)n(n+1)/(n+11) * (n+12)/[6n+1(x-5)n+1(n+2)]
n→inf

equals 1/(6(x-5)) * lim (n+12)(n+1)/(n+11)(n+2)
This limit = 1 so to solve for the x I set
-1<1/6(x-5) and 1/6(x-5)<1 and found the (31/6)<x<(29/6)
but apparently this is incorrect. What am I doing wrong?
 

Answers and Replies

  • #2
Tom MS
27
4

Homework Statement


Find all values of x such that the given series would converge

Σ6n(x-5)n(n+1)/(n+11)

Homework Equations




The Attempt at a Solution


By doing the ratio test I found that
lim 6n(x-5)n(n+1)/(n+11) * (n+12)/[6n+1(x-5)n+1(n+2)]
n→inf
Here it looks like you flipped the wrong fraction.
Ratio test is more like [tex]\lim_{n\rightarrow \infty} {\frac{f(n+1)}{f(n)}}[/tex]
Where [itex]f[/itex] is the function under the sigma. In my understanding, this would flip the fraction the other way from what you have.
 
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