MY NOTES Lets be the sum of the series that has been shown to be convergent by the Integral Test and let ) be the function in that test. The remainder aher n temsis R s- Thus R. is the error made when the sum of the first a terms, is used an an approimation to the total sumsit can be shown that ) de s R, s n 1. Ex) d and 2. + (a) Use the sum of the first 10 terms and Equation 1 to estimate the sum of the series In (Round your answer to sx decimal places) 1549760 How good is this estimate? (b) Improve this estimate using Equation 2 with n10. (Round your answer to six decimal places.) 1.549768 (c) Find a value of n that will ensure that the error in the approximation s , is less than 0.001. n1000

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