Difference between "It develops games to study math" and "It develops games to studying math"
I am studying gerund, and I am getting problems with the rule: "use a gerund after the preposition", but I am confused about the preposition "to", Can you tell me which is the meaning of both sentences?

Question

Difference between "It develops games to study math" and "It develops games to studying math"
I am studying gerund, and I am getting problems with the rule: "use a gerund after the preposition",  but I am confused about the preposition "to", Can you tell me which is the meaning of both sentences?

Answer

"It develops games to study math" - "to" is part of the infinitive form. 
"It develops games to studying math" - to me, it doesn't sound correct. We can use gerund after preposition "to", when "to" is:
a) part of a phrasal verb or some phrasal combination (e.g. I look forward to meeting you), 
b) part of a combination with an adjective (e.g. be addicted to doing sth)
c) part of a combination with a noun (e.g. addiction to gambling).
In your sentence I would use preposition "for" - It develops games for studying math".

Answer

You can say either:
It develops games to study math
It develops games for studying math

Answer

"It develops games to study math" - "to" is part of the infinitive form. 
"It develops games to studying math" - to me, it doesn't sound correct. We can use gerund after preposition "to", when "to" is:
a) part of a phrasal verb or some phrasal combination (e.g. I look forward to meeting you), 
b) part of a combination with an adjective (e.g. be addicted to doing sth)
c) part of a combination with a noun (e.g. addiction to gambling).
In your sentence I would use preposition "for" - It develops games for studying math".