Question

I have a summation formula for Fibonacci numbers.

n
(SUM)F(2i)=F(2n+1)-1
i=0

When the i value is changed from zero, and is then subbed into F(2i)the equation will not work. (RHS wont = LHS)

eg: i=2 n=3

3
(SUM)F(4)=F(7)-1
i=2

I understand the summation bit, (it =3)
But what does it then do to the F(4) part? ie: it becomes: 3F(4).
3*F(4)=9
F(7)-1=12.

What am i supposed to be doing?

Answer 1

Check your typing.

The first few Fibonacci numbers are

1 1 2 3 5 8 13 21 34 55 ...

In the generally accepted notation, these would be F(1)=1, F(2)=1, F(3)=2 etc.
F(0) has no meaning in this general notation.
So let's try your formula for n=3

The i would then go 0,1,2,3
and the Left Side would be
F(0) + F(2) + F(4) + F(6)
which would be ? + 1 + 3 + 8
Right Side = F(7) - 1 = 12
Your formula makes no sense

From where are you getting calculations such as 3F(4) above?