Consider the the following series. [infinity] 1 n3 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.) s10 = (b) improve this estimate using the following inequalities with n = 10. (round your answers to six decimal places.) sn + [infinity] f(x) dx n + 1 ≤ s ≤ sn + [infinity] f(x) dx n ≤ s ≤ (c) using the remainder estimate for the integral test, find a value of n that will ensure that the error in the approximation s ≈ sn is less than 0.0001.