Let denote the Fibonacci sequence such that and . Prove that

**Solution**

It holds that

It follows from Cassini’s identity that

(1)

Setting back at we get

(2)

Since we get

(3)

Hence,

A site of university mathematics

Home » Uncategorized » Fibonacci series

Let denote the Fibonacci sequence such that and . Prove that

**Solution**

It holds that

It follows from Cassini’s identity that

(1)

Setting back at we get

(2)

Since we get

(3)

Hence,