Exercise 6. (*) For the power series, ∞ 1 =2" and n n=1 n32 n=1 discover the disc of convergence, and, furthermore analyse the convergence of the series for each point w in the boundary of the disc of convergence.

Consider the power series (x-2) (x - 2)² 2 + (x - 2)³ 3 3. What is the radius of convergence? (x - 2)¹ 4 1. Write this series as a single sum of the form Σck. (x-2)^. k=1 +... 2. Use the Ratio Test to determine the interval of convergence of this power series.