# Radius of Convergence : Summations and Power Series

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Please see the attached file for full problem description.

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?

https://brainmass.com/math/real-analysis/radius-convergence-summations-power-series-24436

#### 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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