HW #03
Due: 09/20/2023
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Submission Instructions: (Important! If you do not follow them, your paper is not graded.)



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.

Footnotes:

1



a
b
c
d



−1



 
= 1

a db c



d
b
c
a






File translated from TEX by TTH, version 4.03.
On 12 Sep 2023, 21:27.