Is the above equation right? in the other words, can we take the limitation into the summation?

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- Oct 11th 2009, 07:17 PMXingyuanExchangeable of the limitation

Is the above equation right? in the other words, can we take the limitation into the summation? - Dec 30th 2010, 04:25 AMRebesques
Yes, as long as the quantity considered is positive. The worse thing that could happen is that both iterated limits are infinite.

- Dec 30th 2010, 09:21 AMDrexel28
This would be true if converged. As it is stated it doesn't make much sense. But, for example . This is because has radius of convergence from where you can apply Abel's Limit Theorem.