Last Updated：2025/12/06

(mathematics) An infinite series in the form of ∑ₙ₌₀ ᪲(-1)ⁿa_n or ∑ₙ₌₀ ᪲(-1)ⁿ⁺¹a_n, where a_n>0 for all n.

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alternating series

Source Word

alternating series

(mathematics) An infinite series in the form of ∑ₙ₌₀ ᪲(-1)ⁿa_n or ∑ₙ₌₀ ᪲(-1)ⁿ⁺¹a_n, where a_n>0 for all n.

Japanese Meaning

数学において、各項が正と負で交互に現れる無限級数。すなわち、正の値を持つ項が交互の符号（+と−）で並ぶ形の級数のこと。

The alternating series whose term magnitudes decrease monotonically to zero converges by the alternating series test.

項の大きさが単調に減少して0に近づく交代級数は、交代級数判定法により収束します。

Sense（1）

(mathematics) An infinite series in the form of ∑ₙ₌₀ ᪲(-1)ⁿa_n or ∑ₙ₌₀ ᪲(-1)ⁿ⁺¹a_n, where a_n>0 for all n.

alternating series

（ plural ）