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Fall 2005 Math 152 courtesy: Amy Austin (covering sections 10.1, 10.2) 6. Find the sum of the following series. If it diverges, support your answer. a.) a.) an = √ n n+2 c.) d.) b.) an = ln(n) − ln(3n + 1) (−1)n n c.) an = 2 n +1 (−1)n n2 n2 ln n n a.) a4 b.) the limit of the sequence. 3. Determine whether the following sequences are increasing, decreasing, or non monotonic: 1 a.) an = 5 n n2 + 4n + 5 b.) an = n2 ln n c.) an = n d.) an = cos(nπ) Section 10.2 4. Find the first few partial sums of the series ∞ 1 ∞ 1 P P . Try to determine whether they and 2 n=1 n n=1 n converge/diverge. ∞ P n=1 an is a convergent series and n is a formula for the nth partial 2n + 3 sum. What is the sum of the series? sn = 5 + e.) f.) +1 2. Suppose {an } was given to be a convergent se1 quence, a1 = 2, and an+1 = , find: 3 − an 5. Suppose 1 1 − n+5 n+6 n b.) ln n+1 n=2 1. Find the limit of the following sequences, if it exists. If the sequence diverges, state why. e.) an = n=1 ∞ P Section 10.1 d.) an = ∞ P g.) h.) ∞ P 1 n(n + 2) n=1 n−1 ∞ P n=1 ∞ P 2 1 7 n (−5) n=1 2 3 ∞ (−1)n + 3n P n=0 5n ∞ (−1)n 2n P n=2 3n+1 ∞ (−1)n 32n P n=0 i.) 4 + 7n+1 8 16 32 + + + ... 5 25 125