Sequences, Series, and Multivariable Calculus - Handwritten Solution | M 408D, Exams of Mathematics

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M408D (*) Fall 2016 Test2. (1-2) Name .: SoeuT(OW F a“ I. Consider the following power series: s a, = s Cy'eoy n=l n n=l (A) Determine the Radius of Convergence for this series. [2 [a3 ns” _ Bs 3] 4 an (ati) st! (x3) | net ho oe hoe -S<¥-3 65) 80 -2EXL3, Te Radius of Crerginee Is Res (B) Determine the Interval of Convergence of this series. Clecle far CMWergenec ak the endpoint . Ab y= -2, s cutesy" Ss x = 3 L whichisdiinguA since ney pach no" SN ts tle Haunend Sores hey At x =, fous &" aa Lo which is Convergent by the he, h Alkecnatins Serves Testi The Baber 1 lyn ie Cad] = fx[-2 2x 485 Il. For the given convergent series, approximate the summation s to within an error with absolute value less than or equal to 0.0006 . 2 1 - [ Give your solution in two forms: (1) asasum,eg., s ¥ 3 — 3 + 9 , although your solution might have more terms and certainly not these terms, and (2) in decimal form rounded to four (4) decimal places. ] 2a So toe appvevivchan S, 4S how error Suche tat fev ¢ b= 0, cooste ¢ G,0006- Fob rh -b by de “A Sti 9% 7 5% 5¢*7O,Ui 99