交錯級數是正項和負項交替出現的級數,形式滿足a1-a2+a3-a4+.......+(-1)^(n+1)an+......,或者-a1+a2-a3+a4-.......+(-1)^(n)an,其中an>0。在交錯級數中,常用萊布尼茨判別法來判斷級數的收斂性,即若交錯級數各項的絕對值單調遞減且極限是零,則該級數收斂;此外,由萊布尼茨判別法可得到交錯級數的餘項估計。最典型的交錯級數是交錯調和級數。
基本介紹
- 中文名:交錯級數
- 外文名:alternating series
- 表達式:a1-a2+a3-a4-.......+(-1)^(n+1)an
- 套用學科:高等數學
- 適用領域範圍:數學
- 本質:結構最簡單的是正負號相間的級數
定義
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收斂性判別
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典例
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