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....