# Math Induction

• Apr 14th 2007, 09:02 PM
smoothi963
Math Induction
Use to math induction prove:
F1^2 + F2^2 + … + Fn^2 = FnFn+1

• Apr 15th 2007, 12:00 AM
CaptainBlack
Quote:

Originally Posted by smoothi963
Use to math induction prove:
F1^2 + F2^2 + … + Fn^2 = FnFn+1

Not enough information. What is Fk?

RonL
• Apr 15th 2007, 07:06 AM
Plato
This is fairly standard in discrete mathematics courses for the Fibonacci sequence.
• Apr 15th 2007, 10:06 AM
Jhevon
Quote:

Originally Posted by Plato
This is fairly standard in discrete mathematics courses for the Fibonacci sequence.

Yeah, i thought it had something to do with Fibonacci numbers
• Apr 15th 2007, 11:52 AM
Soroban
Hello, smoothi963!

We all assume that these are Fibonacci Numbers.

Quote:

Use induction to prove:

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

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

Assume statement S(k):

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

k+1)² to both sides:

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

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

Factor the right side: .F
k+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, 03:28 PM
smoothi963
Ahh thank you! Yes it is associated with the fibonnaci number, and sorry for not clarifying it. Thanks alot