Transcription of Math 2260 Exam #3 Practice Problem Solutions
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Math 2260 Exam #3 Practice Problem Solutions
Math 2260 Exam #3 Practice Problem Solutions1. Does the following series converge or diverge? Explain your answer. n=02n3n+ :Since 3n+n3>3nfor alln 1, it follows that2n3n+n3<2n3n=(23) , n=02n3n+n3< n=0(23)n=11 23= , the given series Does the following series converge or diverge? Explain your answer. n= :Use the Ratio Test:limn n+13n+1n3n= limn n+ 13n+1 3nn= limn 13 n+ 1n= <1, the Ratio Test implies that this series Does the following series converge or diverge? Explain your answer. n=12nsin(1n).Answer:Notice that the terms of this series are not going to zero:limn 2nsin(1n)= limx 2xsin(1x)= limx sin(1x)12x= limx cos(1x) 2x2 2(2x)2= limx 2 cos(1x)x2 4x2 2= limx 4 cos(1x)= 4where I went from the second to the third lines using L H opital s Rule. Since the limit of the terms isequal to 4, not zero, the series must Does the following series converge or diverge?
Math 2260 Exam #3 Practice Problem Solutions 1.Does the following series converge or diverge? Explain your answer. X1 n=0 2n 3n+ n3: Answer: Since 3 n+ n3 >3 for all n 1, it follows that 2n 3n+ n3 < 2n 3n = 2 3 n: Therefore, X1 n=0 2n 3n+ n3 < X1 n=0 2 3 n = 1 1 2 3 = 3: Hence, the given series converges. 2.Does the following series converge or ...
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