The difference between the partial sum of this function and the natural log is one way of defining the Euler-Mascheroni constant. This function is used to prove that an ant crawling on a continuously growing rope will reach the end. The sum of this function from one to infinity over the integers is 
The difference between the partial sum of this function and the natural log is one way of defining the Euler-Mascheroni constant. This function is used to prove that an ant crawling on a continuously growing rope will reach the end. The sum of this function from one to infinity over the integers is equal to the Riemann zeta function of 1. Its integral diverges when taken from one to infinity in accordance with the p series test, and its antiderivative is (*) ln(x) (EL en of x). This function's graph is a hyperbola whose branches are in the first and third quadrant and whose asymptotes are the x and y axes. This function taken over the natural numbers gives the harmonic series. For 10 points, name this function, which finds the reciprocal of a number.
The difference between the partial sum of this function and the natural log is one way of defining the Euler-Mascheroni constant.
1/x [or one over x; or one divided by x; or x to the negative 1; accept harmonic series at any time before mention; accept any letter instead of x; accept reciprocal until mention, prompt after]