Fibonacci Number as Sum of Binomial Coefficients/Mistake/Second Edition
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Source Work
1997: David Wells: Curious and Interesting Numbers (2nd ed.):
- The Dictionary
- $5$
Mistake
- Lucas discovered a relationship between Fibonacci numbers and the binomial coefficients:
- $F_{n + 1} = \dbinom n 0 + \dbinom {n - 1} 1 + \dbinom {n - 2} 1 + \cdots$
Correction
The given expression is a misprint for:
- $F_{n + 1} = \dbinom n 0 + \dbinom {n - 1} 1 + \dbinom {n - 2} 2 + \cdots$
Interestingly and oddly, this is correct in the first edition of Curious and Interesting Numbers of $1986$.
Sources
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $5$