# How do you find the taylor series for #lnx# in powers of #x-1#?

##### 2 Answers

#### Explanation:

The general formula for the Taylor series of a function

we can immediately note that:

so the constant term is null. For the following terms, we have to calculate the derivatives of

and we can easily see that in general:

and for

The Taylor series is then:

As a bonus, we can note that this expansion can be used to calculate the sum of the alternating harmonic series:

In fact if we use the Taylor series above for

#### Explanation:

Using

Is the Taylor series for