Alternating Series/Examples/General Form

Examples of Alternating Series

Let $S_n$ be a real series of the form:

$\ds S_n = \sum_{k \mathop \ge 0} \paren {-1}^k p_k$

or:

$\ds S_n = \sum_{k \mathop \ge 1} \paren {-1}^{k - 1} p_k$

where:

$\forall k \in \N: p_k > 0$


Then $S_n$ is an alternating series.


Sources

  • 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): alternating series
  • 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): alternating series
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