Question

Find a power series whose sum is:

(a) 5 / (1-3x)

(b) 9 / (1-4x)

(c) 6 / (2-4x)

Answer 1

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.

Answer 2

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.