- Thread starter
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- #1
- Jan 26, 2012
- 995
Thanks to those who participated in last week's POTW!! Here's this week's problem!
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Problem: One defines the Fibonacci sequence by $F_1=1,\,F_2=1,\,F_{n+2}=F_n+F_{n+1}$ for $n\geq 1$. Show that for all $n\in\mathbb{N}$, $F_{n+1}^2-F_nF_{n+2}=(-1)^n$.
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Remember to read the POTW submission guidelines to find out how to submit your answers!
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Problem: One defines the Fibonacci sequence by $F_1=1,\,F_2=1,\,F_{n+2}=F_n+F_{n+1}$ for $n\geq 1$. Show that for all $n\in\mathbb{N}$, $F_{n+1}^2-F_nF_{n+2}=(-1)^n$.
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Remember to read the POTW submission guidelines to find out how to submit your answers!