Question

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4. [0/10 Points] DETAILS LARCALC11 9.9.501.XP. 1/2 Submissions Used Find a power series for the function, centered at c. Rx) = 5 * C = -2 00 f(x) = n=0 Determine the interval of convergence. (Enter your answer using interval notation.) I Submit Answer Viewing Saved Work Revert to Last Response [10/10 Points] DETAILS LARCALC11 9.R.060. 2/2 Submissions Used Use the Alternating Series Test, if applicable to determine the convergence or divergence of

Answer 1

Solution : Power series of the function centered at c. > fex) = are ;C= -2 So the power series is given by a a(rc)" provided T-(r-c) 18- ci a is the first teem & r-c is the comman ratio. 4 5-(x+2) - nzo where 4 So, 5-r a 445 I-r 4. 5-(x+2) 11 - $(143)} a = 45. = 5 (2+2) → ro So, 4 5-1 I am (1) (+6142) nzo M20 n 노 5-n -> Ž 4 (t) (x+2) mo ntl = E 4 5-n 6) (x+2) nEO required Powerseries. nt n So, fex) = 2 4651) (x+2) n=o series converges when & lutalci » Int21 25 -5L2+2 <5 con -72x23 So, the intervel of onvergence, | (-7,3) Scanned with CamScanner