math104-f21:hw6
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| 4. Show that if a series $\sum_n a_n$ converges absolutely, then $\sum_n a_n a_{n+1}$ converges absolutely. | 4. Show that if a series $\sum_n a_n$ converges absolutely, then $\sum_n a_n a_{n+1}$ converges absolutely. | ||
| - | 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 $\lim_n b_{n+1} / b_n = \lim_n b_n^{1/n} = 1$. | + | 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 $b_n$, such that $\lim_n b_{n+1} / b_n = \lim_n b_n^{1/n} = 1$. |
| ====== Solution ====== | ====== Solution ====== | ||
math104-f21/hw6.1633758004.txt.gz · Last modified: 2026/02/21 14:43 (external edit)
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