Chapter 10.4, Problem 19E

What is the radius of convergence for the power series (see image)

Find the sum of the series. Determine whether it diverges or converges. Please show work process.

(-1)"3" (4n + 2)2 п Find the interval of convergence for the power series >, n=0

OSelect the FIRST correct reason why the given series converges. A. Convergent geometric series B. Convergent p series c. Comparison (or Limit Comparison) with a geometric or p series D. Alternating Series Test E. None of the above (n + 1)(8)" 1. 32n (-1)" 2. 7n + 5 n=1 00 3. (-1)"- n+3 7(7)" A 4. 2n sin (4n) 5. n? (-1)" In(e") n² cos(na) 00 6.

Consider the series (-10)"-1 14" n=1 Determine whether the series converges, and if it converges, determine its value. Converges (y/n): y Value if convergent (blank otherwise):

Find the radius of convergence of the power series. (-1)"x" En=0| SM

Help solving problem and finding interval

(3x - 1)" n Consider the power series a) Show that the resulting series when x = 0 is conditionally convergent. b) Find the radius and interval of convergence of the power series. n=1

7. Consider the power series (-1)*+1g" n2 n=1 (a) The series converges when |x| R. Find R. (b) Does the series converge when x = R? What about when x = -R? Explain.