- #1
bfpri
- 12
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So i need to prove f0f1 + f1f2...f2n-1f2n=f2n2 where fn is the n-th fibonacci number..
Attempting to solve this i let n=k . Then k=1 and f22=1 which is 1=1 so that is true.
Then i show if the statement is true for k then it is true for k+1, that is f0f1 + f1f2+f2k-1f2k+f2kf2k+1+f2k+1f2k+2= f2k+22 .
I then simplify
f0f1 + f1f2+f2k-1f2k+f2kf2k+1+f2k+1f2k+2
= f2k2+ f2kf2k+1+f2k+1f2k+2.
Now I'm stuck..How do i simplify this to f2k+22 ?
Thanks
Attempting to solve this i let n=k . Then k=1 and f22=1 which is 1=1 so that is true.
Then i show if the statement is true for k then it is true for k+1, that is f0f1 + f1f2+f2k-1f2k+f2kf2k+1+f2k+1f2k+2= f2k+22 .
I then simplify
f0f1 + f1f2+f2k-1f2k+f2kf2k+1+f2k+1f2k+2
= f2k2+ f2kf2k+1+f2k+1f2k+2.
Now I'm stuck..How do i simplify this to f2k+22 ?
Thanks