They didn't accept my invitation at first, but I________ persuade them at last.
考查情态动词。 could 是 can 的过去式,比 can 委婉,表示能够,但做了不一定成功; might 表示可能; be able to 表示通过努力做成功了某事。由persuade them at last 可知选 B 。