I define one of the most important constants in mathematics, the Euler-Mascheroni constant. It intuitively measures how far off the harmonic series 1 + 1/2 + ... + 1/n is from ln(n). In this video, I show that the constant must exist. It is an open problem to figure out if the constant is rational or irrational.

Application: Integral fractional part of 1/x from 0 to 1:    • Integral of the fractional part of 1/x  

Monotone Sequence Theorem:    • Monotone Sequence Theorem  
Series playlist:    • Series  
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