Ab. L.
asked • 11/04/16How many terms of the series do we need to add in order to find the sum to the indicated accuracy? The series, from n=1 to infinity, of (-1^(n+1))/(n^6).
Indicated accuracy => the abs. value of the error must be less than .00005 . I got n=5. Not sure if it's correct.
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1 Expert Answer
Kenneth S. answered • 11/04/16
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Please describe the details of how you obtained n=5.
Because the absolute values of this series decrease from term to term and the signs of terms alternate,
I think you have to solve 1/n6 < 0.00005 which is equivalent to
n6 > 20,000 so n > sixth root of 20,000. n> 5.21
Therefore n = 6.
Ab. L.
got b sub6=absolute value is less than 0.00005. Therefore, the first five terms of the series are needed to find the sum of the indicated accuracy.
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11/04/16
Ab. L.
Is that the right answer? Would it not be 1/(n+1)^6 < 0.00005 ?
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11/04/16
Ab. L.
Would it not be 1/(n+1)^6 < 0.00005 ? Is n= 6 the correct answer? I really want to learn. Thanks. I really appreciate it. (:
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11/04/16
Kenneth S.
The use of exponent n+1 is just for sign assignment of the term. The absolute value is all you need, so what I did was set n-6 < 0.00005 and solved that.
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11/05/16
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Ab. L.
11/04/16