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是通过从调和级数中移除所有包含单个数字 
的项而获得的级数。 令人惊讶的是，虽然调和级数发散，但所有 10 个 Kempner 级数都收敛。 例如，
其中 
的数字不包含字符串 314。 此总和的近似值为 
。 一般来说，当从求和的 
中排除长度为 
的特定字符串时，
近似由 
给出 (Baillie 和 Schmelzer 2008)。