I began feeling better after I started eating this way,so I

I began feeling better after I started eating this way,so I continued to do so.
这句意思是 当我开始像这样吃的时候,我开始感觉好多了,所以我会继续这么做
do so 就相当于eating this way 而继续按照这个吃法不是一直都在在吃,
continued doing so 是不停的做某事,不间歇地 ,显然只有continued to do so.符合 用不定式表示按这种方法做
再问： this way为什么不加冠词in?
再答： eating是及物动词 可直接加 this way,不需要加介词