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This document presents two theorems regarding necessary and sufficient conditions for the interchange of limit and summation for sequences of infinite series. Theorem I states that for a double sequence where the sum of terms converges for each n and the limit of the sequence equals x for each p, a necessary and sufficient condition for the sum of x to converge to the limit of the sum of x is that the series of x is uniformly convergent. Theorem II similarly states that for m > 0, a necessary and sufficient

Author

elham

Language

EN