# Abel's Limit Theorem

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## Theorem

Let $\sequence {a_i}$ be a convergent series.

The limit which is assigned by the Abel summation method exists and equals the sum of the series.

## Proof

## Also see

## Source of Name

This entry was named for Niels Henrik Abel.

## Sources

- 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*... (previous) ... (next): Entry:**Abel's limit theorem** - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**Abel's Limit Theorem**