A guess of series

**Xingyuan** · September 22nd 2009, 06:19 PM

Whether the series $\sum_{n=1}^{\infty}a_{n}$ convergence or not ,
can we get the conclusion $\sum_{n=1}^{\infty}o(a_{n}) = o(\sum_{n=1}^{\infty}a_{n})$ ?
can someone give a prove of it or a counter-example?

**Laurent** · September 23rd 2009, 04:12 PM

Originally Posted by Xingyuan

Whether the series $\sum_{n=1}^{\infty}a_{n}$ convergence or not ,
can we get the conclusion $\sum_{n=1}^{\infty}o(a_{n}) = o(\sum_{n=1}^{\infty}a_{n})$ ?
can someone give a prove of it or a counter-example?

What is $o(\sum_{n=1}^{\infty}a_{n})$ supposed to mean? (the little o notation is indexed by a variable, like $o_n(a_n)$ in the left hand side, so what should the variable be here??)

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