Thread: Math Induction

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







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

Originally Posted by smoothi963

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



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

Not enough information. What is Fk?

RonL

This is fairly standard in discrete mathematics courses for the Fibonacci sequence.

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

Hello, smoothi963!

We all assume that these are Fibonacci Numbers.

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.

Ahh thank you! Yes it is associated with the fibonnaci number, and sorry for not clarifying it. Thanks alot