Being a League member, he is always helping others. 和To be a League member, he is always helping others.有什么区别呢？

being a League member, he is always helping others. 作为一名共青团员，他总是帮助其他人。（动词ing形式表状态，已经是一名团员了）
To be a League member, he is always helping others.为了成为一名共青团员，他总是帮助其他人。（不定式，表目的、将来。还不是团员，为了以后成为团员。）
语法解析：
这题考查非谓语动词。对于非谓语，各个语法书讲解不一。一般我把非谓语分成三部分：
动词不定式 to do 基本语法意义：表目的，表将来；
To pass next exam, he works hard. 为了通过下一场考试，他努力学习。

动词ing形式 V+ing 基本语法意义：表进行，表状态；
Singing a song, he walked into his classoom. 他【唱着歌】走进了他的教室。
He finished his homework, tiring but exciting. 他完成了他的家庭作业，疲惫并兴奋着。

动词的过去分词 基本语法意义：表过去，表被动。
Criticized by Tom, Bob went away. 被汤姆批评了一顿，鲍勃走了。

非谓语动词其他的用法大体可以分为三类：
与动词的固定搭配（平时注意积累）
stop to do forget to do mean to do try to do devote to doing
stop doing forget doing mean doing try doing look forward to doing
固定句式
It's time for sb to do sth.
主语+have nothing to do but do
习惯用法
Seeing is believing.