Thursday, 3 August 2017

Can we pull out a constant of a divergent series?

I know that if a series converges, the following applies:




n=ican=cn=ian



However, I can't seem to find any info on whether this holds for diverging series as well. The property is often mentioned together with this one, of which I know it does not apply to divergent series:



n=ian+bn=n=ian+n=ibn




This makes me think the first property might require the same condition, but I'm not sure.

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