Formula for Sum of Odd Fibonacci Terms

The Fibonacci sequence is defined by  
\[F_1=F_2=1, F_{n+1}=F_{n-1}+F_n, n \ge 2\]
.   (1)
Proof is by induction. Let  
  be the statement that (1) is true for  
. Then  
  is true since  
Suppose that  
  is true. Then

  to both sides.

by the definition of the Fibonacci sequence. Hence  
  is true and the theorem is proved.

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