I do not understand the difference among following"

subject+ verb+ to do
subject +verb+ comma +doing
subject +verb+ for doing

the first is used to show a purpose: I learn gmat to learn MBA

the second is used to show method and effect of main verb. any more? pls, add.

I learn gmat, making my english better.
I learn gmat, doing homework every day

what is for the third case.
I learn gmat for taking MBA.

pls help to fullfill the usages of the 3 cases and comment.