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# (a) Use the sum of the first 10 terms to estimate the sum of the series $\sum_{n = 1}^{\infty} 1/n^2.$ How good is this estimate?(b) Improve this estimate using (3) with $n = 10.$(c) Compare your estimate in part (b) with the exact value given in Exercise 34.(d) Find a value of $n$ that will ensure that the error in the approximation $s \approx s_n$ is less than 0.001.

## a) $1.54977, \quad$ error $\leq 0.1$b) 1.6452222c) 0.000288d) $n>1000$

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Missouri State University

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University of Michigan - Ann Arbor

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