Evaluate the product

**Solution**

We are making use of the identity

Hence,

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# Tag: Product

## A finite product

## An eta Dedekind type product

## An infinite product with Lucas and Fibonacci numbers

## Telescopic Fibonacci product

## An infinite product

A site of university mathematics

Evaluate the product

**Solution**

We are making use of the identity

Hence,

Prove that

**Solution**

Let and . Hence,

Let denote the -th Fibonacci number and the – th Lucas. Prove that

**Solution**

Exploiting the fact that we deduce that .

**Lemma: **Let be positive numbers. It holds that

*Proof: *Making use of Binet’s formula we have successively:

by cancellations and the fact that . This completes the proof of the lemma.

Setting we get the result.

Let denote the Fibonacci sequence. Prove that

**Solution**

Let denote the partial product. Thus,

Prove that

**Solution**

We simply note

and the result follows.