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sept0909 - Math 1502 D September 9 2009 1 School of...

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Unformatted text preview: Math 1502 D, September 9 2009 1 School of Mathematics Math 1502 Georgia Tech Calculus II, Section D Quiz # 3 September 9 2009 First Name : Last Name : −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− 1. Transform the first expression into the second by a change of indices (Check ALL details carefully ! !) 25 n=2 (−1)n ; n−1 24 k =1 (−1)k+1 k 2. Find the sum of the series (Hint : transform it as a telescopic sum.) ∞ n=3 1 = n(n − 1) Math 1502 D, September 9 2009 2 3. Find the sum of the series (Hint : use the geometric series.) ∞ j =0 (−1)j x2j = 4. Are the following series convergent or not ? (Indicate explicitly the test used to conclude. Be careful there is a trap !) (a) n + 117 ( n 3 + 4n 2 ) 5 / 6 (b) √ 5n + 3 cos nπ/ 3 ( n 3 + 4n 2 ) 1 / 3 ...
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sept0909 - Math 1502 D September 9 2009 1 School of...

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