Using a geometric series to make a power series

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Last updated 2:31 AM on 6/13/26
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What is the form we are trying to turn the geometric series into

1/(1-x) and then you sub the “x” that you derive into xn. Then you have the magnitude of x less than 1 to solve for the radius of convergance.

<p>1/(1-x) and then you sub the “x” that you derive into x<sup>n</sup>. Then you have the magnitude of x less than 1 to solve for the radius of convergance.</p>
2
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How does multiplying a power series by xsomething affect the radius of convergence

It does not affect it at all

3
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<p>What do you have to do when finding the power series from a geometric series and it is centered at a=(-1)</p>

What do you have to do when finding the power series from a geometric series and it is centered at a=(-1)

Then you want to change the form you are trying to rearrange the geometric series into. ( you want (X+1) instead of just x)

<p>Then you want to change the form you are trying to rearrange the geometric series into. ( you want (X+1) instead of just x)</p>
4
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<p>Solve</p>

Solve

<p></p>