Let \[a_{1}, a _{2}......\] be a Fibonacci series.
I have a book which has a problem under the "mathematical induction" chapter, which asks me to prove
\[a _{n+1}^{2}=a _{n}a _{n+2}=(-1)^{n}\]
I think the statement is incorrect. For n=1, we don't have the statement correct, and I can't expect it to be correct for n>1 as \[(-1)^{n}\] will always only have values either +1 or -1, and the expression \[a _{n}a _{n+2}\] will have increasing value.
Do you think I am correct, or is there really a prove for the statement.
Please provide me some help.

See more answers at brainly.com

\[a_{n+2}a_n-a_{n+1}^2=(-)^n\]is a true statement.

But the statement given there is not correct, am I right?

So your '=' sign is not a typo.?

Looking for something else?

Not the answer you are looking for? Search for more explanations.

## More answers

Looking for something else?

Not the answer you are looking for? Search for more explanations.