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exam_3_s07

# exam_3_s07 - is convergent ﬁnd its limit 2 Let p n be the...

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1. Define the sequence { a n } by setting a 1 = 1 and a n +1 = 1 1 + a n for n 1. Assuming that
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Unformatted text preview: is convergent, ﬁnd its limit. 2. Let { p n } be the sequence of prime numbers, i.e. { p n } = { 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , . . . } . Show that ∞ X n =1 (-1) n +1 p n converges. 3. Find a power series representation for the function g ( x ) = x x-5 in powers of x and state for which values of x this representation is valid. 4. Find the interval of convergence of the power series ∞ X n =1 x n 3 n n 1 / 2 . Don’t forget to check for convergence at the endpoints of the interval! 5. Determine if the series converges or diverges. If it converges, determine if this convergence is absolute or conditional. a. ∞ X n =1 (-1) n n + 1 n 3-3 n 2 + 9 n + 13 b. ∞ X n =1 ± n 2 + 1 2 n 2 + 1 ² n c. ∞ X n =2 1 n (ln n ) 2 d. ∞ X n =1 (-1) n +1 4 √ n + 1 e. ∞ X n =1 (-1) n n n + 5 f. ∞ X n =1 1 5 + (-3) n Calculus II, Exam 3 Work Page...
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