Posted by John on Sunday, April 5, 2009 at 3:34pm.
Find a power series whose sum is:
(a) 5 / (13x)
(b) 9 / (14x)
(c) 6 / (24x)

PreCal  Reiny, Sunday, April 5, 2009 at 4:22pm
suppose I have
1 + x + x^2 + x^3 + ...
this is a geometric series with
a = 1 and r = x
S_{∞} = a/(1r)
= 1/(1  x)
so in a) you have
5/(13x)
this would match the terms
5 + 5(3x) + 5(3x)^2 + 5(3x)^3 + ...
You did not state whether you have to give the answer in Sigma notation, but I am pretty sure you could change it into that notation, if you study series at this level.
for c), simplify
6/(24x) to 3/(1  2x) and proceed as above.

PreCal  John, Sunday, April 5, 2009 at 5:55pm
MY ANSWERS:
(a) ax = 5(3x)^(x1)
(b) ax = 4(4x)^(x1)
(c) ax = 3(2x)^(x1)
I'm confused because all of those series have a divergent sum, and it looks like they're each supposed to be convergent.
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