What different nuisance is conveyed in the following forms:
공부하기 위해 학교에 가고 있다
공부하러 학교에 가고 있다
공부하려고 학교에 가고 있다
The translations for both are: I’m going to school to study
But is there any meaning difference embedded in the forms ?
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The meaning is more or less the same since they all indicate the purpose.
The difference is in formality and usage context.
VERB-기 위해 = in order to VERB. Most formal, so mostly used in writing.
VERB-러 = to VERB. Only used with movement verbs like come, go, or attend.
VERB-려고 = to VERB. General, all-around phrase for "to VERB" or "wanting to VERB".
So sentences like 좋은 학교에 들어가러 열심히 공부했다 sounds a little strange. It should be 들어가려고 (or 들어가기 위해서 more formally).