おかげで・幸い・幸いなことに: the difference
おかげでN3
Meaning
Thanks to, Because of
Past papers
Tested 8 times in past papers
Example
薬のお陰でだいぶよくなりました。
Thanks to the medicine, I got much better.
Meaning
Luckily, Fortunately
Past papers
Example
幸いなことに遊ぶ時間が結構ある。
Fortunately, I have quite a lot of time to enjoy myself.
How to tell them apart
「幸いなことに」: pure luck, a lucky escape; stresses chance.
「おかげで」: credit to a person or thing: 「先生のおかげで合格できた」 (Thanks to my teacher, I passed).
In business letters, 「〜幸いに存じます／幸いです」 is a polite way to request something; it often appears in reading and listening.