“服理”常见且地道的英文表达可以是 “be convinced by reason” 或 “accept reason” ，以下为你具体分析：
be convinced by reason： “be convinced by”表示“被……说服”，“reason”意思是“道理；理性；理由” ，整个短语直接传达出被道理说服的含义，和“服理”意思高度契合。例如：He was finally convinced by reason and admitted his mistake.（他最终被道理说服，承认了自己的错误。 ）
accept reason： “accept”有“接受；承认”之意，“accept reason”即“接受道理”，也就是“服理”的意思。例如：You should accept reason and stop arguing.（你应该服理，别再争论了。 ）