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Fibonacci Numbers. The Fibonacci numbers are 1,1,2,3,5,8,13,21,….1,1,2,3,5,8,13,21,…. We can define them inductively by f1=1,f1=1, f2=1,f2=1, and...

Fibonacci Numbers.

The Fibonacci numbers are

1,1,2,3,5,8,13,21,….1,1,2,3,5,8,13,21,….

We can define them inductively by f1=1,f1=1, f2=1,f2=1, and fn+2=fn+1+fnfn+2=fn+1+fn for n∈N.

Prove that fn=[(1+√5)n−(1−√5)n]/2n√5.

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