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发帖数: 368 | 1 ☆─────────────────────────────────────☆
okla (IP~IC~IQ卡，统统告诉我密码) 于 (Sun Aug 14 17:07:39 2005) 提到:
Ahlfors said that the convergence of \sum a_n is neither sufficient nor
necessary condition for the convergence of \prod (1+a_n).
(a_n are complex numbers)
I've worked out the example that \prod (1+a_n) converges but \sum a_n doesn't.
For example, a_n=-1/(n+1), \sum a_n -> -\infty, but \prod (1+a_n) -> 0
Actually, as long as for all a_n, -1 < a_n < 0, then \prod (1+a_n) is positive
and decreasi |
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