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sum of Fibonacci numbers ...
Posted:
Nov 20, 1999 4:28 PM


My question is:
If F_n is the nth Fibonacci number, find a simple expression for F_1 + F_2 + ... + F_n which involves F_p for only one p.
Doesn't this sum just reduce to F_(n+2)  2 ??? To prove this I think I could use induction (would this be the best way to do this?). Or does this arguement show the result?...
Let S=F_1+F_2+...F_n Make sum left and right sides below F_1=1 F_2=F_1+1 F_3=F_2+F_1 F_4=F_3+F_2 ........... F_n=F_(n1)+F_(n2) ____________________ S = 1+SF_n+1+SF_(n1)F_n=2+2SF_nF_(n+1) from above
S=F_(n+2)  2
Thank you for your time & assistance, Kathleen



