• anonymous
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.
Mathematics

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