quiz6ws2009

# quiz6ws2009 - a ∞ X n =0 cos nπ 5 n b ∞ X n =1 ln ± n...

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Quiz 6 Instructor: Stephan Spencer 24 March, 2009 Student Name: 1. Determine whether the following sequences converge or diverge. If they converge, ﬁnd the limit. a). a n = n + 3 n 2 + 5 n + 6 b). a n = ( - 1) n ± 1 - 1 n ² c). a n = sin 2 n 2 n d). a n = ln( n + 1) n e). a n = n ! n n f). a n = ( - a ) n n ! g). a n = ± n n + 1 ² n h). a n = 1 n Z n 1 1 x dx 2. Determine whether the following series converge or diverge. a). 1 - 1 2 + 1 4 - 1 8 + ··· b). X n =1 1 + 3 n 2 n c). X n =0 ± 2 n +1 5 n ² d). X n =1 ± ln(3 / 2) ln 2 ² n 1

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3. Write the following as a telescoping sum and ﬁnd the sum a). X n =1 4 (4 n - 3)(4 n + 1) b). X n =1 ± n + 1 - n n 2 + n ² 4. Use the divergence test to determine whether the series may converge or diverge. There is no need to determine the value.
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Unformatted text preview: a). ∞ X n =0 cos( nπ ) 5 n b). ∞ X n =1 ln ± n 2 n-1 ² c). ∞ X n =1 arctan n d). ∞ X n =1 ± 3 5 n-2 n ² 5. For what values of x, if any, does the series converge? a). ∞ X n =0 (-1) n x 2 n b). ∞ X n =0 (-1 / 2) n ( x-3) n 6. Use the integral test, if possible, to determine whether the series converges or diverges. a). ∞ X n =1 arctan n n 1 . 1 b). ∞ X n =1 √ n n 2 + 1 c). ∞ X n =2 1 n (ln n ) 2 d). ∞ X n =1 n n 4 + 1 2...
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quiz6ws2009 - a ∞ X n =0 cos nπ 5 n b ∞ X n =1 ln ± n...

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