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5
votes
3answers
147 views
Closed form for the sum of even fibonacci numbers?
I recently took a look a project euler, and I am trying to think of a smart way to do number 2. I looked at the sequence, and I saw that the question is basically asking for
$$
\sum_{i=1}^n F_{3i}
$$
...
4
votes
4answers
476 views
Closed form solution of Fibonacci-like sequence
Could someone please tell me the closed form solution of the equation below.
$$F(n) = 2F(n-1) + 2F(n-2)$$
$$F(1) = 1$$
$$F(2) = 3$$
Is there any way it can be easily deduced if the closed form ...
2
votes
1answer
96 views
Finding n in Fibonacci closed loop form
The nth term of the Fibonacci series is given by
$F_{n}$=$\Big\lfloor\frac{\phi^{n}}{\sqrt{5}}+\frac{1}{2}\Big\rfloor$
How do you get the following expression for n from this?
...
