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### sp01q2

Course: MATH 153, Spring 2008
School: Ohio State
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# QUIZ 2 MATH 153 SP01 Name (2p): .................................... 1. Check convergency and, if possible, find the sum for [n2 - (n + 2)2 ] n=1 Answer: Check general term: n2 - (n + 2)2 = n2 - (n2 + 4n + 4) = -4n - 4 - (since n ); hence, since the general term DOES NOT converge to 0, the series is DIVERGENT. Of course, no need to check the sum here. 2. Same problem for the series (.1)n n=0 Answer: Notice...

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# QUIZ 2 MATH 153 SP01 Name (2p): .................................... 1. Check convergency and, if possible, find the sum for [n2 - (n + 2)2 ] n=1 Answer: Check general term: n2 - (n + 2)2 = n2 - (n2 + 4n + 4) = -4n - 4 - (since n ); hence, since the general term DOES NOT converge to 0, the series is DIVERGENT. Of course, no need to check the sum here. 2. Same problem for the series (.1)n n=0 Answer: Notice that the series is a geometric series - hence in this case we can skip the checking of the "general term converging to zero" procedure 1 1 - and since the general term is (0.1)n = ( 10 )n , where 10 < 1 we have that the series is convergent. than More that, based on the formula for the sum of the geometric series, we have that 1 (.1)n = n=0 1 - 0.1 3. Check convergency for the series: (-1)n ] n Answer: Again, check the general term; (-1)n lim 1 - = n n (-1)n = lim 1 - lim = n n n =1-0=1 where for the second term we use Squeeze theorem, for (-1)n oscillates between 1 and -1, and so the afore-mentioned theorem is the one to be used: (-...

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Ohio State - MATH - 153
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Ohio State - MATH - 153
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Ohio State - MATH - 153
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Ohio State - MATH - 153
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Ohio State - MATH - 131
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Ohio State - MATH - 131
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Ohio State - MATH - 131
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Ohio State - MATH - 131
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Ohio State - MATH - 131
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