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Answer :
Final answer:
To estimate the value of the series ∑(2/n^1.1) with an error of at most 0.0001, you would need at least 2015 terms.
Explanation:
To estimate the value of the series ∑(2/n^1.1) with an error of at most 0.0001, we need to find the number of terms required. The formula for the error term in an alternating series is given by |a(n+1)|.
In this case, |a(n+1)| = |2/(n+1)^1.1|. We want this term to be less than or equal to 0.0001, so:
|2/(n+1)^1.1| ≤ 0.0001
Solving this inequality, we find that n+1 ≥ (2/0.0001)^(1/1.1).
Using a calculator, we can find that (2/0.0001)^(1/1.1) ≈ 2015.6. Therefore, the value of n should be at least 2015.
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