I have an infinite series, let's say Σa(adsbygoogle = window.adsbygoogle || []).push({}); _{n}, and I can split it into Σb_{n}+ Σc_{n}. If one of the series is convergent (let's say Σb_{n}) while the other is divergent (Σc_{n}), is it safe to say that the original series (Σa_{n}) is also divergent?

If to show an example, I have:

[tex]\sum {\frac{1+n}{1+n^2}} = \sum {\frac{1}{1+n^2}} + \sum {\frac{n}{1+n^2}}[/tex]

Intuitively, I can say that yes, but is this enough?

Or maybe just for cases where both of the series are either negative or positive (positive in this case)?

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# Convergence of series

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