(n choose 0)*F(0) + (n choose 1)*F(1) + ... + (n choose n)*F(n)=F(2n) I'm beginning to think induction is a bad approach...
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Originally Posted by veronicak5678 (n choose 0)*F(0) + (n choose 1)*F(1) + ... + (n choose n)*F(n)=F(2n) I'm beginning to think induction is a bad approach... Let , then a common fact (Binet's formula) says that . Thus, That said, a quick check shows that and . So that the above shows
A couple more proofs here. A more general form would be: ( setting you get the particular case above).
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