Please see attachment. I am having trouble expanding the factorial. I know that the ratio test must be applied to retrieve the radius of convergence, and ultimately the interval of convergence.

Question

anonymous · Answer

attachment

anonymous · Answer

The question says:
If k is a positive integer, find the radius of convergence, R, of the series

anonymous · Answer

$$\frac{((n+1)!)^{k+8}}{((n)!)^{k+8}}=(n+1)^{k+8}$$ this is because they all have the same exponent so they cancel nicely

anonymous · Answer

$$\lim_{n\to \infty}\frac{((k+8)(n+1)!)}{((k+8)n)!}= 0 $$ you don't have to expand this one, just evaluate the limit

anonymous · Answer

See (attempt: hopefully it is clear enough) http://i1270.photobucket.com/albums/jj613/Abducens_Nucleus/MAT036-MQ16.png @AugustineSextus @AccessDenied @eliassaab @asnaseer @ParthKohli

anonymous · Answer

Unfortunately, that was incorrect.

anonymous · Answer

@eliassaab
Professor, consider this very similar worked out problem. 


@amistre64
@TuringTest
@Callisto 
@agentc0re

anonymous · Answer

@hamza_b23 
@lgbasallote 
@mahmit2012 
@experimentX
@Calcmathlete

anonymous · Answer

The answer for the radius of convergence is not 0.

anonymous · Answer

The answer is (k+8)^(k+8), but how?

anonymous · Answer

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