Assignment
1. Determine the convergence or divergence of the following infinite series and give a reason for your answer.
A) n-1∑∞ (2/n3)
B) n-0∑∞ 6(1/3)n
C) n-1∑∞ (n + 2) / (2n - 3)
2. Determine whether the following infinite series converges using the ratio test:
n=1∑∞ n3n / n!
3. Find the interval of convergence of the power series
n=0∑∞ (x/2)n
4. Write the first 5 terms of the MacLaurin Series for the function
f (x) = xe2x
5. Solve the separable DE yy' - 2ex = 0 subject to the initial condition y(0) = 3.
6. Solve the first order linear DE y' + 2xy = 10x subject to the condition y(0) = 8.