Show that converges for all values of z in the disk D(-1)={z:abs(z+i)<2} and diverges if abs(z+i)>2. abs() means absolute value.
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Originally Posted by splash Show that converges for all values of z in the disk D(-1)={z:abs(z+i)<2} and diverges if abs(z+i)>2. abs() means absolute value. This is a power series centered at Use the generalized ratio test for power series. That is, That means the series converges absolutely when is strictly less then reciprocal of 1/2=2. Thus, ---> converges (absolutely) ---> diverges
Last edited by ThePerfectHacker; November 3rd 2006 at 08:33 AM.
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