# For my Friend Kushagra Sahni! 20 Dec

Algebra Level 3

$\large a<{ \left( 1+\frac { 1 }{ n } \right) }^{ n }<b$

If above inequality is true for all positive integers $$n,$$ then what positive integers $$a$$ and $$b$$ minimize the quantity $$|b - a|?$$ Give your answer as $$a+b.$$

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