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Unformatted text preview: Name: 56 whens. Perm No: Section Time : Math 5C  Midterm 2 March 1, 2007
Instructions: 9 This exam consists of 5 problems worth 10 points each, for a total of 50 possible points 9 You must Show all your work and fully justify your answers in order to recieve full credit, You may leave your answers in unsimpiiﬁed form, unless the emblem asks you
to simplify o No books or calculators are allowed You may use a one—sided page of notes“ a Write your answers on the test itself, in the space slotted You may attach additional
pages if necessary, 1. Consider the sequence {enhzg given by 815 32 1 3’ 9 ’ 27’ ' H (a) Find a. formula fo: the nth team an of this sequence in terms of '11, starting with
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Ck? LH‘ e‘czrm=0\o= L1 WW“ =—.. Lita/33‘" Hr W24) (13) Does the sequence {Graham} converge or diverge? If it converges, ﬁnd its iimitn SW \H: 773'“ {’Huww A 3m 0.
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((2) Find the sum of the series 2 an, or Show that it diverges. an
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\I?) 2, Do the series below converge or diverge? J ustify your answer's 00 Tl A ﬁlm
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V\=~.\ 3. Find the radius and interval of convergence of the power series if: 2”($ ~1)"
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4‘ Find the Taylor series for f (51:) = W, centered at m = 1, and determine its radius of ﬁ (For full credit, your answez Shouid be written in E—notation To receive partial credit,
you may write out the ﬁrst ﬁve terms of the Taylor series.) :: {"1" m QM ==\ convergence \ “ﬂ: 3:: 1 t
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5‘ (3,) Find the function ﬁx) Whose Maclam’in seIies is 2 71:0 . (Hint: Multiply the series by a: and then differentiate) N
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(13) Use (a) to evaluase the sum ; (n :1)?”
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Z (““31“ T" Z W“ '3” .. SEE A.)
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