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.

Add comment

Security code