Determine the convergence or divergence of infinite series

Question

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) = xe^2x

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.