Use to math induction prove:

F1^2 + F2^2 + … + Fn^2 = FnFn+1

Please help. Im stuck at the inductive step >.<

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- Apr 14th 2007, 08:02 PMsmoothi963Math Induction
Use to math induction prove:

F1^2 + F2^2 + … + Fn^2 = FnFn+1

Please help. Im stuck at the inductive step >.< - Apr 14th 2007, 11:00 PMCaptainBlack
- Apr 15th 2007, 06:06 AMPlato
This is fairly standard in discrete mathematics courses for the Fibonacci sequence.

- Apr 15th 2007, 09:06 AMJhevon
- Apr 15th 2007, 10:52 AMSoroban
Hello, smoothi963!

We all assume that these are Fibonacci Numbers.

Quote:

Use induction to prove:

. . (F1)² + (F2)² + (F3)² + … + (Fn)² .= .(Fn)·(Fn+1)

I assume you've verified statement S(1) already.

Assume statement S(k):

. . (F1)² + (F2)² + (F3)² + ... + (Fk)² .= .(Fk)·(Fk+1)

Add (Fk+1)² to both sides:

. . (F1)² + (F2)² + (F3)² + ... + (Fk+1)² .= .(Fk)·(Fk+1) + (Fk+1)²

The LHS is the left side of S(k+1).

Factor the right side: .Fk+1·(Fk + Fk+1) . = .(Fk+1)·(Fk+2)

. . . . . . . . . . . . . . . . . . . \_______/

. . . . . . . . . . . . . . . . . . . this is Fk+2

. . and we have the RHS of S(k+1).

And the inductive proof is complete.

- Apr 15th 2007, 02:28 PMsmoothi963
Ahh thank you! Yes it is associated with the fibonnaci number, and sorry for not clarifying it. Thanks alot