Question

Find R, the radius of convergence, and the open interval of convergence for:

Σ The series has the open interval of convergence of (-2,2). Determine if the series converges or diverges at each endpoint to find the full n=1 interval of convergence. n. .2" At x = -2 the series converges At x = 2 the series diverges The interval of convergence is M

Answer 1

o Criven that the series a an n-an nal 4) nal no -24 Converger for (-2,2). At x==2(left-end point), the soues becomes 62) 7.211 o on which converger by Alternating At x= 2 right end point), the series n test series becomes 22 na nel n. 2n p-series test which diverges by Hence interval of convergence [-2,2).) =