Consider the power seriesf(z) =∑∞k=0akzkwhereak=(2k,keven,17kkodd. (a)Show that neither limn→∞an+1annor limn→∞|an|1nexist. (b)Find the radius of convergence of...

Consider the power seriesf(z) =∑∞k=0akzkwhereak=(2k,keven,17kkodd.

(a)Show that neither limn→∞an+1annor limn→∞|an|1nexist.

(b)Find the radius of convergence of each power series:f1(z) =∞∑m=022mz2mandf2(z) =∞∑m=0z2m+172m+1.

(c)Verify thatf(z) =f1(z) +f2(z). Use the radii of convergence off1(z)andf2(z)to infer theradius of convergence off(z)

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Expert Solution

The radius of convergence of is . The solution is attached

Colby Messinger answered 2 hours ago

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