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2224Test3AReview

# 2224Test3AReview - MATH 2224 PRACTICE PROBLEMS FOR...

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MATH 2224: PRACTICE PROBLEMS FOR TEST #3 (Set 1) 1. Find the interval of convergence of each of the following power series (open interval only): a. n n 1 n n 2 n ) 2 x ( ) 1 ( ! ! " # = b. " # = + ! 0 n n 1 n ) 2 x 3 ( 2. For the series " # = 1 n 3 n 1 find the first three terms of the sequence of partial sums associated with the series. 3. Rewrite as a triple integral in rectangular coordinates: \$ % & % % & ’ ’ ( ( % d d d cos sin 2 0 2 / 0 cos 4 0 3 4. Find the sum of the geometric series: " # = ) * + , - . 1 n n 4 3 2 5. Use the definition of convergence to find the exact sum of the series " # = / 0 1 2 3 4 + ! + 1 n 1 n 2 1 3 n 2 1 . (Your answer should show that you know the definition of what it means for a series to converge.) 6. Does the sequence 5 6 7 8 9 : + 1 n n ln converge? If so, to what? Use the definition of convergence to show whether or not the series " # = + 1 n 1 n n ln converges. (Note: i.e., consider n n S lim # ; ) 7. Find the value of m for which the geometric series ! + ! + ! 27 m 2 9 m 2 3 m 2 2 3 2 converges to 5.

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