# How do you find the limit of mathematical series ?

##### 2 Answers

That depends on the series. There are several different kinds of techniques we can use for the different types of series.

#### Explanation:

Do you have any examples?

This series does not converge (it does not have a limit).

#### Explanation:

The series in question is the sum of

The first few terms are:

At first glance, the series seems to converge - which means after you take all of its terms and add them up, you get a number. However, take a look at this series:

The first few terms are:

This is called the harmonic series, and it is known to diverge - i.e. the sum keeps getting bigger and bigger as

Compare the first few terms of the harmonic series with our series:

Our series is bigger than the harmonic series after

What this means is that our series is larger than the divergent harmonic series, so the sum of our series should be larger than the sum of the harmonic series . But that means our series diverges too - it will just get bigger and bigger as