Explain how to find the sum of an infinite harmonic series.

To find the sum of an infinite harmonic series, use the formula S = a/(1-r), where a is the first term and r is the common ratio.

An infinite harmonic series is a series of the form 1/1 + 1/2 + 1/3 + 1/4 + ... + 1/n + ..., where n approaches infinity. To find the sum of this series, we can use the formula for the sum of an infinite geometric series, which is S = a/(1-r), where a is the first term and r is the common ratio.

In this case, the first term is 1/1 = 1, and the common ratio is 1/2, since each term is half of the previous term. Therefore, we have:

S = 1/(1 - 1/2)
S = 1/(1/2)
S = 2

So the sum of the infinite harmonic series 1/1 + 1/2 + 1/3 + 1/4 + ... is 2. This means that as we add more and more terms to the series, the sum gets closer and closer to 2, but never actually reaches it. This is an example of a convergent series, since the sum approaches a finite value as the number of terms increases.