Originally Posted by

**hockey777** So Let n=1

$\displaystyle l_{1}=f_{0}+f_{2}$

1 = 0 +1

Check

Assume $\displaystyle l_{n}=f_{n-1}+f_{n+1}$

$\displaystyle l_{n+1}$=$\displaystyle l_{n} + l_{n-1}$ stated in our first assumption

$\displaystyle l_{n}= f_{n-1}+f_{n+1}$ and *$\displaystyle l_{n-1}=f_{n-1}+f_{n+1}$*

$\displaystyle l_{n+1}=f_{n-1}+f_{n+1} +f_{n-1}+f_{n+1}$

then by simplifying with Fibonacci Identities I get

$\displaystyle l_{n+1} = f_{n} + f_{n+2}$ for n≥1.

My question now is with the part between the **, can I make that assumption based on my induction assumption since that is n-1 and my induction assumption is n.