I'm sorry I forgot __ (write) down your telephone number.

问题描述:

I'm sorry I forgot __ (write) down your telephone number.

to write.
forget to do 忘记做某事(那个do没发生)
forget doing 忘记做过某事(那个do表示的动作有发生)

To write

to write
因为forgot to do 是忘了做某事,某事还没有做
而forgot doing 是忘记做了某事,某事已经做了.
相同的用法还有regret等.

应该填to write.
因为这里是forget to so sth.
表示“忘记做某事了”。