Consider the following series. Σ n6 n = 1 (a) Use the sum of the first 10 terms to estimate the sum of the given series.

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Consider the following series. Σ n6 n = 1 (a) Use the sum of the first 10 terms to estimate the sum of the given series. (Round the answer to six decimal places.) $10 = 1.017342 (b) Improve this estimate using the following inequalities with n = 10. (Round your answers to six decimal places.) Sn + f(x) dx SSS S + Jn + 1 "", 1° f(x) dx 1.017343 <S< 1.017344 (C) Using the Remainder Estimate for the Integral Test, find a value of n that will ensure that the error in the approximation s s, is less than 0.0000001. On > 0 On> 11 On > 6 On > 18 On > -18