One page for each problem (a total of 2 pages). 50 % Penalty if not followed.
Make a single PDF file. File name: hw_03_doe_john.pdf.
Email the PDF file to me5331exam@gmail.com with the subject line: Doe, John, HW#3
1. (a) Determine whether the following series converges or diverges.
∞ ∑ n=2
⎛ ⎝
2 + n ln
⎛ ⎝
n − 1
n + 1
⎞ ⎠
⎞ ⎠
(b) If the series converges, numerically sum the series (take, say, first
1,000 terms). If the series is divergent, you can say so and skip this problem.2.
Find a set of roots for the following simultaneous equations
using the Newton-Raphson method.
21 x + ex sin y = 3
(1)
− x2 + 1 7 y = 6.
(2)
Start with (x0, y0) = (1, 1) as an initial guess and mention the number
of iterations to reach convergence1.
You have to show the formulas you derived to implement the Newton-Raphson method.
You can attach a code that you wrote but it's not necessary.