Originally Posted by
muglyhacker I am currently re-viewing some text books of a course I took a few years ago and have come across this Fibonacci relation in the form Fn = Fn+2 Fn+1
F0 = F2 - F1
F1 = F3 - F2
F2 = F4 - F3
Fn = Fn+2 Fn+1
Adding LHS together we get LHS = F0 + F1 + F2 +
+ Fn
and RHS = F2 - F1 + F3 - F2 + F4 - F3 +
+ Fn+2 Fn+1
And using telescoping cancellation the book states that the RHS = Fn+2 - 1
I can only get the RHS to = Fn+2 Fn+1 - 1 (Because F1 = 1). I am stuck with the Fn+1 term of the RHS; nothing I can see cancels it out, yet clearly the book states that it has gone. Unfortunately the book doesnt clearly show the cancellation in steps. Anyone here like to help, am I being very dumb???
(sorry about the formatting; I subscripted all the numbers but it doesn't seem to cut and paste into this)