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Sequence
2016


Problem - 3943
The Fibonacci sequence (Fn)n0 is defined by the recurrence relation Fn+2=Fn+1+Fn with F0=0 and F1=1. Prove that for any m, nN, we have Fm+n+1=Fm+1Fn+1+FmFn. Deduce from here that F2n+1=F2n+1+F2n for any nN

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