I need help with the following:
We are given the series $\sum_1^\infty \frac{a_n}{5^n}$ and $\sum_1^\infty \frac{(-1)^na_n}{5^n}$ . We also know that the first series converges while the second one diverges. Now we must answer these questions:
1) is series $\sum_1^\infty \frac{a_n}{5^n}$ a)absolutely convergent or b)conditionally convergent?
2) is the series $\sum_1^\infty \frac{a_n}{4^n}$ a)absolutely convergent, b)conditionally convergent, c) divergent
3) is the series $\sum_1^\infty \frac{a_n}{6^n}$ a)absolutely convergent, b)conditionally convergent, c) divergent
4) What is the radius of convergence of is the series $\sum_1^\infty (n+1)a_nx^n$
1b) seems obvious and I can easily see that 2a) is wrong by the comparison test. But how can I find the exact answer? I tried using the series test, but it doesn't give me information about conditional divergance.
Any help would be appreciated