Exam III - Calculus for Scientists and Engineers II - Spring 2004 | MATH 112, Exams of Mathematics

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MACS112 Spring 2004 Name: Exam II Section: In order to receive full credit, SHOW ALL YOUR WORK. Full credit will be given only if all reasoning and work is provided. Enclose your final answers in boxes, 2. 1. (8 points) Consider the sequence whose nth term is given by a, = a »n=1,2,3,.... (a) Determine whether this sequence converges or diverges. If it converges, find its limit. Dim (HH © [Lt ne pC nr?) | LL (b) Does the series ¥) an converge or diverge? Explain. nel Me Gince Mm a =| £0, @ by Divergence “lest. Vie oo 2. (16 points) Find the sum of the following convergent series: oe oe w n od @ Se 25s 2, - &(¢) * 3 (" rs oS nd Lo the germetric Web adgue wo he a, EL 7 + ae TE? SP Fay ged Welk} +! © ar glee O Ine a =f, 8 le Bre 3A + Bet 28 nLOFATB)ED mows %. b> A428 YER, @=71 oO wt LL, Lo 2 we. yes Sa* fy -X) SAVE + a x ¥o- g wl 1 os o A wi-