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Topic: sum of Fibonacci numbers ...
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Kathleen

Posts: 58
Registered: 12/6/04
sum of Fibonacci numbers ...
Posted: Nov 20, 1999 4:28 PM
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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_(n-1)+F_(n-2)
____________________
S = 1+S-F_n+1+S-F_(n-1)-F_n=2+2S-F_n-F_(n+1)
from above

S=F_(n+2) - 2



Thank you for your time & assistance,
Kathleen





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