4. [40.11 Points] DETAILS SCALCET9 11.8.AE.001. 0/100 Submissions Used MY NOTES ASK YOUR TEACHER Example a: For what values ofx does the series 2 (X ' 3)" converge? n = 1 n Solution _ 1') Let an = . Then we get the following. n an + 1 = . L an (X - 3)\" 1 = |:""3"i \"5"\" By the Ratio test, the given series is absolutely convergent, and therefore convergent, when IX 3| D . Now .H... .. Dw-MD .. [3 C] . The Ratio Test gives no information when |x 3| = 1, so we must considerx = 2 and X = 4 separately. If we putx = 4 in the (-1)" n series, it becomes 2 i, the harmonic series, which is divergent. If x = 2, the series is E , which -Select c by the n Alternating Series Test. Thus the given power series converges for 2 C? c x ? c 4. Need Help? 5. [40.11 Points] SCALCET9 11.8.011. Oi'l 00 Submissions Used MY NOTES ASK YOUR TEACHER Find the radius of convergence, R, of the series. Find the interval, 1, of convergence of the series. (Enter your answer using interval notation.) Need Help? _ 6. [40.11 Points] DETAILS SCALCET9 11.8.013.MI. 0/100 Submissions Used MY NOTES ASK YOUR TEACHER Find the radius of convergence, R, of the series. xn+4 n 24m R=| Find the interval, I, of convergence of the series. (Enter your answer using interval notation.) Need Help? 7. [I0.11 Points] DETAILS SCALCET9 11.XP.8.009. 011 00 Submissions Used MY NOTES | ASK YOUR TEACHER I Find the radius of convergence, R, of the series. 9\"x"' 2 2 Find the interval, 1, of convergence of the series. (Enter your answer using interval notation.) Need Help? 8. [-IO.11 Points] DETAILS SCALCET9 11.8.021.MI. 0/100 Submissions Used MY NOTES ASK YOUR TEACHER Find the radius of convergence, R, of the series. w 2 (x 2)\" \"=0 n2+1 Find the interval, 1, of convergence of the series. (Enter your answer using interval notation.) I= Need Help? 9. [-ID.11 Points] DETAILS SCALCET9 11.XP.8.D12. 0l100 Submissions Used MY NOTES ASK YOUR TEACHER Find the radius of convergence, R, of the series. 2 (1)""\"4)" \"=0 3n+1 Find the interval, 1, of convergence of the series. (Enter your answer using interval notation.) 1: Need Help? _'' 10. [-IO.11 Points] DETAILS SCALCET911.XP.8.D13.MI. 0/1 00 Submissions Used MY NOTES ASK YOUR TEACHER Find the radius of convergence R of the series. 2 5\"(x + 4)\" J; n=1 Find the interval of convergence I of the series. (Enter your answer using interval notation.) 1= Need Help?