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I want to write “Sorry for the inconvenience caused” at the end of an email to a Japanese colleague. How do I say it?

Answer by Japanese teacher

woman-answer

(1) ご迷惑（めいわく）をおかけして、すみません。
Gomeiwaku o okakeshite, sumimasen.
Sorry for the inconvenience caused
(2) ご迷惑（めいわく）をおかけして、申（もう）し訳（わけ）ございません。
Gomeiwaku o okakeshite, sumimasen.
Sorry for the inconvenience caused

Explanation

Both expressions mean “I apologize for the inconvenience caused”.
However, the second expression is more polite because “mooshiwake gozaimasen” (sorry) is the humble form of “sumimasen”.
By humbling oneself, you can increase the level of respect for the other person and indirectly show how apologetic you are in causing the inconvenience.