- Thread starter
- #1

#### ATroelstein

##### New member

- Jun 30, 2012

- 15

$$\frac{5 + \sqrt{5}}{2\sqrt{5}}*(\frac{1 + \sqrt{5}}{2})^{x}

$$

From looking at it, it seems like it could be simplified so that the right-hand side of the multiplication would be:

$$(\frac{1 + \sqrt{5}}{2})^{x+1}

$$

I started to pull the left-hand side apart to get a match to the right-hand side and ended up with:

$$

(\frac{4}{2\sqrt{5}} + \frac{1}{\sqrt{5}} * \frac{1+\sqrt{5}}{2}) * (\frac{1 + \sqrt{5}}{2})^{x}

$$

From here, I'm starting to wonder if my initial observation was flawed. Is there a way to simplify this is terms of:

$$(\frac{1 + \sqrt{5}}{2})^{x+1}

$$

Thanks.