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Jolly into doing
Colloquial Usage
The phrase is casual and best suited for informal conversations, not formal documents or professional settings. 
Subtle Persuasion
It implies a gentle form of persuasion that makes an activity seem fun, not forceful or demanding. 
Positive Connotation
Using 'jolly into doing' often conveys a positive vibe and light-hearted tone in the persuasion. 