Posted by **John** on Sunday, April 5, 2009 at 3:34pm.

Find a power series whose sum is:

(a) 5 / (1-3x)

(b) 9 / (1-4x)

(c) 6 / (2-4x)

- Pre-Cal -
**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/(1-r)

= 1/(1 - x)

so in a) you have

5/(1-3x)

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/(2-4x) to 3/(1 - 2x) and proceed as above.

- Pre-Cal -
**John**, Sunday, April 5, 2009 at 5:55pm
MY ANSWERS:

(a) ax = 5(3x)^(x-1)

(b) ax = 4(4x)^(x-1)

(c) ax = 3(2x)^(x-1)

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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