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Math 152 - Spring 2010 Assignment 10 Due on April 14, 5: Show that the ratio Test is inconclusive but the Root Test indicates convergence for the...

Show that the ratio Test is inconclusive but the Root Test indicates convergence for the series
1/2 + 1/3^2 + 1/2^3 + 1/3^4 + 1/2^5 + ...

Math 152 - Spring 2010 Assignment 10 Due on April 14, 5:30 1. Show that the ratio Test is inconclusive but the Root Test indicates convergence for the series 1 2 + 1 3 2 + 1 2 3 + 1 3 4 + 1 2 5 + ... 2. (a) Find a power series representation for the arctangent function Note: You may use the fact that (arctan x ) 0 = 1 1+ x 2 . (b) Deduce from the arctangent series that π = 6 3 X n =0 ( - 1) n 2 n + 1 ± 1 3 ² n . 1
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