(5 pts) Determine whether the following series is absolutely convergent, conditionally convergent, or divergent. Show your work.
∑_{n=1}^{∑} (-1)^{n-1} n / (3n^2 + 2)
For what values of x is the power series convergent? Find the interval of convergence of the series.
∑_{n=1}^{∑} (2x - 1)^n / (5^n ∙ ∙n)
3)determine true or false
T F If lim_{n→∑} a_n = 0, then ∑_{n=1}^{∑} a_n converges;
T F If ∑_{n=1}^{∑} a_n diverges, then lim_{n→∑} a_n ≠ 0;
T F If ∑_{n=1}^{∑} |a_n| converges, then ∑_{n=1}^{∑} a_n converges;
T F If a_n < b_n for all n ≥ 1 and ∑_{n=1}^{∑} b_n diverges, then ∑_{n=1}^{∑} a_n diverges;
T F If lim_{n→∑} |a_n| = 0, then lim_{n→∑} a_n = 0.