What is the difference between "learn to do"&"learn doing"?
Betty is going to learn to dance from now on.
Betty is going to learn dancing.

Question

Answer

In the first sentence "dance" is a noun. In the second, "dance" is a verb.
They have the same meaning.

Answer

"Betty is going to learn to dance from now on."  In this sentence 'to dance' is the infinitive.  It is a verb. 
"Betty is going to learn dancing."  In this sentence "dancing" is a gerund.  It seems like a verb, but it's acting like a noun.  You could take a noun and put in there and it would make sense.

Evden çıkmadan dil öğrenme fırsatını kaçırmayın. Deneyimli dil eğitmenlerimizden oluşan seçkimize göz atın ve ilk dersinize şimdi kaydolun!