(a) Determine whether the following series converges or diverges. 8 (2+ n=2 2 + n ln (n-1)) +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 + e* sin y = 3 - x + 17 y = 6. (1) (2) Start with (xo, yo) = (1, 1) as an initial guess and mention the number of iterations to reach convergence. 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.