# Fibonacci sequence

1. Aug 30, 2008

### Euler_Euclid

if $$a_1, a_2, a_3 .............$$ belong to the fibonacci sequence, prove that

$$a_1a_2 + a_2a_3 + ............ + a_{2n-1}a_{2n} = (a_{2n})^2$$

2. Aug 30, 2008

### uart

If you are familiar with mathematical induction then that's the way to go with this one. Using the recursion equation ($a_{2n} + a_{2n+1} = a_{2n+2}$ etc) should let you make the inductive step fairly easily.

BTW. Is this homework ?

3. Aug 30, 2008

### Euler_Euclid

not at all!!!

4. Aug 30, 2008

### uart

Are you familar with mathematical induction?

5. Aug 30, 2008

### Euler_Euclid

Is there any other method other than this?