Lưu ý rằng không có truy cập vòng số nguyên, như trong Đối với truy cập = Bắt đầu để chấm dứt loại cấu trúc vòng lặp. Nếu một số nguyên truy cập là cần thiết, bạn sẽ phải khởi tạo bên ngoài vòng lặp, và tăng nó bên trong vòng lặp. | 74 EXCEL NUMERICAL METHODS A I B . c D E I 10 X F x exact F x calc error 11 1 12 13 1 term 16 14 30 89 2 terms 15 16 3 terms Figure 4-2. Evaluation of Taylor series. CHAPTER 4 NUMBER SERIES 75 Problems Answers to the following problems are found in the folder Ch. 04 Number Series in the Problems Solutions folder on the CD. 1. Evaluate the following infinite series a 1 2 b 1 n2 c 1 n 2. Evaluate the following 5 1 1 - 1 2 1 3 - 1 4 . 3. Evaluate the following infinite series Eczx where a 1 X 1 4. Evaluate the following s 1 2 1 3 5. Evaluate the following s 1 2 - 1 3 6. Evaluate Wallis series for 7t J 2n 2 2n - l 2n 1 over the first 100 terms of the series. 7. Evaluate Wallis series for 7t summing over 65 536 terms. Use a worksheet formula that uses ROW and INDIRECT to create the series of integers. 8. A simple yet surprisingly efficient method to calculate the square root of a number is variously called Heron s method Newton s method or the divide-and-average method. To find the square root of the number a 1. Begin with an initial estimate X. 2. Divide the number by the estimate . evaluate a x to get a new estimate 3. Average the original estimate and the new estimate . x d x 2 to get a new estimate 76 EXCEL NUMERICAL METHODS 4. Return to step 2. Use this method to calculate the square root of a number. The value of the initial estimate X must be greater than zero. 9. In the divide-and-average method the better the initial estimate the faster the convergence. Devise an Excel formula to provide an effective initial estimate. 10. The series y 16 -1 1 y 4 -l 1 2k -1 5 2k-ỵ fa 2k -1 23 92 -1 proposed by Machin in 1706 converges quickly. Determine the value of 7t to 15 digits by using this .
