I'm looking to find and then prove by induction a formula for F1 + F3 + F5 +F7 + .... I recognize that the series 1, 2, 5, 13, 34, 85, 233 follows the formula: F(n) = F(n-2) + (F1 + F3 + F5 + ... + F(n-2)). I'm not sure if this is the formula I'm looking for and I'm not sure how to set up such a formula for proof by induction. Can anyone help at all? Thanks.
2007-01-28 19:44:07 · 2 answers · asked by Jesse 2 in Science & Mathematics ➔ Mathematics
If you're familiar with the Fibonacci series, and you do a few of these sums, you'll notice that the results a the even Fibonacci numbers. Prove the n=1 case, then show that if (F1+F3+ ... + F(n)) = F(n+1), then the next series (through F(n+2)) must sum to F(n+3). Which is actually quite easy using the definition of Fibonacci numbers (F(n+3) = F(n+2) + F(n+1)).
2007-01-28 19:57:11 · answer #1 · answered by Hal 2 · 1⤊ 0⤋
It's 89 not 85.
What are you exactly looking for? You know there is a whole journal devoted to Fibonacci numbers?
2007-01-28 20:03:21 · answer #2 · answered by gianlino 7 · 0⤊ 1⤋