The article discusses different formulas to estimate the sum of Harmonic Series, focusing on improving upon Euler's formula. By using the infinite harmonic series and the Euler-Mascheroni constant, the researchers found better approximations for finite harmonic series. They also explored the Leibniz series for Pi and identified a correction factor using Euler numbers. Each new approximation in the study outperformed previous ones, tailored to different types of harmonic series. While the correction factor for the Leibniz series may not have practical applications, it offers insights into infinite harmonic series.