Radius of convergence of the power series

Question

Assignment:

Radius of Convergence of the Power Series

Theorem :- _{n = 0}Σ^∞ a_nzⁿ  is a power series and _{n = 1}Σ^∞na_nz^n-1    is the power series obtained by differentiating the first series term by term. Then the derived series has the same radius of convergence as the original series.

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