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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