This problem has been bothering me for some time. Any thoughts or insights are greatly appreciated.(adsbygoogle = window.adsbygoogle || []).push({});

Consider a function, f, with continuous third derivative on [-1,1]. Prove that the series

[itex]\sum^{\infty}_{n=1} (nf(\frac{1}{n})-nf(-\frac{1}{n}) - 2\frac{df}{dn}(0))[/itex] converges.

Thanks in advance for any help!

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# Convergence of a general series

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