# Substitution mania

**Number Theory**Level 3

We all know the sum of the below expression \[\displaystyle{\sum _{ n=1 }^{ k }{ \frac { 1 }{ n } } \approx \ln { k } +\Upsilon +\frac { 1 }{ 2k } }\] So the value of \[\displaystyle{\sum _{ n=0 }^{ 27 }{ \frac { 1 }{ n } } }\] can be approximated to **K** . Find **K**

**DETAILS**

\(\Upsilon \) is known as Euler's Mascheroni constant who's decimal approximation is **0.5772....**