Practice Midterm 2

Practice Midterm 2 - 1 Determine whether the series is convergent or divergent You may use any of the tests we covered(a(10 points n= n=1 n2n(1

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1. Determine whether the series is convergent or divergent. You may use any of the tests we covered. (a) (10 points) Σ n = n =1 n 2 n (1 + 2 n 2 ) n (b) (10 points) Σ n = n =1 3 n - 1 2 n + 1 (c) (10 points) Σ n = n =1 n 2 + 1 n 3 + 1 (d) (10 points) Σ n = n =1 ( - 5) 2 n n 2 9 n 2. (20 points) Determine whether the series is absolutely convergent, con- ditionally convergent, or divergent. You may use any of the tests we covered. Σ n = n =2 ( - 1) n n ln ( n ) 3. (10 points) Suppose f ( x ) is a positive decreasing function and let a n = f ( n ), n 1. Draw a picture which explains how to rank the following three quantities in increasing order i 4 1 f ( x ) dx, Σ i =3 i =1 a i , Σ i =4 i =2 a i 4. (20 points) Find the radius of convergence and the interval of conver- gence. Σ n = n =1 2 n ( x - 2) n ( n + 2)! 1
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5. Suppose Σ n = n =0 c n x n converges for x = - 3 and diverges for x = 5. What can be said about the convergence/divergence of the following series? Why?
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This test prep was uploaded on 04/07/2008 for the course MATH 1 taught by Professor Johns during the Spring '08 term at NYU.

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Practice Midterm 2 - 1 Determine whether the series is convergent or divergent You may use any of the tests we covered(a(10 points n= n=1 n2n(1

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