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# Radius of Convergence : Summations and Power Series

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a) Evaluate

b) What is the radus of convergence ....
....
To what simple function does this series converge?
c) Is f(z)=...
...
analytic near z= -1? and expand f(z)=
...
in a power series near z= -1 can we predict the domain of convergence from the outset?

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#### Solution Preview

See attachment please!

a. Evaluate and

Solution. (1) By a formula for n-th derivative

we know that

if ; otherwise, since is analytic at .
. ...

#### Solution Summary

Convergenc of series is investigated. The solution is detailed and well-presented.

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