She is writing a letter to a friend of hers,______ him to attend the party.

She is writing a letter to a friend of hers,______ him to attend the party.
A.to invite B.inviting
填哪一个啊,______ 处作什么语?to do可以用作补足语,而doing不可以
谁能解释一下怎么辨别补足语啊,举个例子也可以.