Let denote the
– th Fibonacci number. Prove that:
.
.
.
Solution
- Taking partial sums we see that the series telescopes:
- Using Cassini’s identity we note that:
- Combining the previous results we have successively:
The result follows.
A site of university mathematics
Let denote the
– th Fibonacci number. Prove that:
Solution
The result follows.
Prove that
Solution
We have successively:
Let denote the Fibonacci sequence. Prove that
Solution
Let denote the partial product. Thus,
Let such that
and
. Prove that
.
Solution
We have successively:
Prove that
Solution
We recall the product identity
Thus,