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Proving the Root Test

A) Prove root test " lim(sqrt|An)|)=L as n goes to infinity" assuming ratio test "lim(|An+1)|/|A n|)=L as n goes to infinity"

ps. {An} is a sequence of non-zero complex numbers

b) Prove that although the following power series have R=1 sum(nz^n) does not converge on any point of the unit circle.

Solution Summary

The root test is proven assuming ratio test.