Proof: Fibonacci Sequence Sums to Squares

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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
 
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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 ?
 
not at all!
 
Are you familar with mathematical induction?
 
Is there any other method other than this?
 

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