Mia L.

asked • 04/04/16

Find a power series representation for the following:

Find a power series representation for the following:
 

3x / (2 - x) , centered at 1

1 Expert Answer

By:

Douglas N.

6/(1-y) does not equal (1 + y + y2 + y3 + ... ), it equals 6(1 + y + y2 + y3 + ... ).
 
I would go with
 
3x/(2-x) = -2 + ∑n>=16(x - 1)n
 
or equivalently
 
3x/(2-x) = -3 + ∑n>=06(x - 1)n
 
Also, this answer only holds for 0 < x < 2, as the series only converges on that interval, where |x -1| < 1.
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04/04/16

Douglas N.

In my comment above,
 
3x/(2-x) = -2 + ∑n>=16(x - 1)n
 
should be
 
3x/(2-x) = 3 + ∑n>=16(x - 1)n
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04/04/16

Roman C.

tutor
Thanks for the correction. I rushed because there was only a short time window for me at that moment.
 
You are right that we should report a convergence interval.
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04/06/16

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