Let G be a group, A be a group of all elements in G that have a finite order.

Prove that the quotient group G/A contains no elements of finite order.

Hmmm... If I assume that there is a gA in G/A for which there exists a natural n so that |gA|=n , then I get that : gA+...gA=gA (n times)

How do I continue ? Am I doing this right?

Thanks!