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Unformatted text preview: (ii) When every term a n is a positive number and all partial sums of the series n =1 a n are smaller than 24, then it must be the case that the series converges. (iii) If follows from the Ratio Test that the series n =1 1 n diverges. ***THERE ARE MORE PROBLEMS ON THE BACK SIDE O THIS PAGE*** . 3. (a) (10 points ) There is a number b such that 1 + (1 / 3) + (1 / 3) 2 + (1 / 3) 3 + + (1 / 3) 200 = 1b 1(1 / 3) . What is that number b ? (b) (15 points) Find a positive integer n such that  e(1 + 1 + 1 2 + 1 3! + + 1 n ! )  < 1 10 . Explain using the Taylor Remainder Formula why your answer is correct. 4. (a) (10 points) Compute lim x 1cos( x 4 ) x 8 . (b) (10 points) Compute f (1 / 3), if f ( x ) = x + x 2 2 + x 3 3 + x 4 4 + . . . ....
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This note was uploaded on 04/03/2010 for the course MATH 20 taught by Professor Staff during the Fall '08 term at Maryland.
 Fall '08
 staff
 Math

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