## Example 8.4.18 (d): Finding Taylor Series by Integration

Start with a known series and integrate both sides.

### Example

Which function is represented by the series*1/n x*^{n}Our known series with which to start is, once again, the Geometric series.
For variety, let's use *t* as variable:

^{1}/_{1-t}= t^{n}= t^{n-1}

Integrating both sides gives:

^{1}/_{1-t}dt = t^{n-1}dt = t^{n-1}dt = 1/n x^{n}

Thus, the function represented by this series is:

1/n x^{n}=^{1}/_{1-t}dt = -ln(1-x)

1/n x^{n}f(x) = -ln(1-x)