In this Section we consider power series. These are examples of infinite series where each term contains a variable, x , raised to a positive integer power. We use the ratio test to obtain the radius of convergence R , of the power series and state the important result that the series is absolutely convergent if | x | < R , divergent if | x | > R and may or may not be convergent if x = ± R . Finally, we extend the work to apply to general power series when the variable x is replaced by ( x x 0 ) .


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