Question

1. Consider the power series 1 X cn(x 2)n: n=0 It is known that the power series converges when x = 5 and diverges when x = 3. Is it possible the radius of convergence R is (a) R = 2? Yes (b) R = 4? Yes (c) R = 5? Yes Brie y justify your answers. 2. Use the identity 1 1 x No No No 1 X = xn ( ) n=0 and term-by-term di erentiation or integration to nd power series representations for (a) f(x) = 1 xx2 . (b) g(x) = ln(1 x) Find the interval and radius of convergence for these series