# Random Harmonic Series

Random Harmonic Series

Multiply each term in the harmonic series by a plus or minus sign, which was randomly chosen by flipping a fair coin. The result is a random variable called the random harmonic series. In this Demonstration, we approximate the density of the random harmonic series by simulation. The original infinite sum is replaced by a finite sum, and such a sum is calculated at least ten thousand times. The Demonstration shows a histogram of the values of the sums and a kernel density estimate. The Demonstration can also show a series of special approximate densities (see Details).