## An infinite product

- Tolaso J Kos
- Administrator
**Posts:**867**Joined:**Sat Nov 07, 2015 6:12 pm**Location:**Larisa-
**Contact:**

### An infinite product

Let $\mathcal{F}_n$ denote the $n$ -th Fibonacci number and $\mathcal{L}_n$ the $n$ – th Lucas. Prove that

$$\prod_{n=1}^{\infty} \left ( 1 + \frac{1}{\mathcal{F}_{2^n +1} \mathcal{L}_{2^n+1}} \right ) = \frac{3}{\varphi^2}$$

$$\prod_{n=1}^{\infty} \left ( 1 + \frac{1}{\mathcal{F}_{2^n +1} \mathcal{L}_{2^n+1}} \right ) = \frac{3}{\varphi^2}$$

**Imagination is much more important than knowledge.**

**Tags:**

## Create an account or sign in to join the discussion

You need to be a member in order to post a reply

## Create an account

Not a member? register to join our community

Members can start their own topics & subscribe to topics

It’s free and only takes a minute

## Sign in

### Who is online

Users browsing this forum: No registered users and 0 guests