Substitution mania

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....

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