### Limits : Proving the Root Test Assuming the Ratio 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.