Random Harmonic Series

upper bound of sum

100

simulated sums

10000

new simulation

1

bin for histogram

0.2

bandwidth for density

0.2

show approximate densities

g

n

0

1

2

3

4

5

6

7

all 8

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).