MAT136H1 Study Guide - Midterm Guide: Improper Integral

• School: UTSG
• Department: Mathematics
• Course: MAT136H1
• Professor: all

Document Summary

Question #4 (medium): estimating the sum of series and its error. Based on the first n number of terms in the series, the sum can be estimated. The error is than what remains from the next term thereafter until infinity. This is calculated by and its lower and upper limit can be set using improper integral: Use the sum of the first 7 terms to approximate the sum of the series. The sum of the first 7 terms is: . Now that since the range that fluctuates is between 0 and 1. The error is the amount of deviation of the above estimate based on actual calculation of 7 terms from the true value of the series. This error amount is equal to the remainder starting from the 8th term onward to infinity.