Due next Thursday, 10/7, 6pm

1. Calculate (a) $\lim (n!)^{1/n}$, (b) $\lim (n!)^{1/n}/n$

2. Show that if a series $\sum_n a_n$ absolutely converges, then $\sum_n a_n a_{n+1}$ converges absolutely.

3. Ross Ex 14.1 (briefly describe your reasoning)

4. Ross 14.4

5. Give an example of divergent series $\sum_n a_n$ of positive numbers $a_n$, such that $\lim_n a_{n+1} / a_n = \lim_n a_n^{1/n} = 1$. And give an example of convergent series $\sum_n b_n$ of positive numbers $a_n$, such that $\lim_n b_{n+1} / b_n = \lim_n b_n^{1/n} = 1$.