Question: The Fibonacci Sequence is defined using the recursive definition Fn$+2$ Fn$+1+$ Fn$,$ with Fo $=0$ and F$1=1=$ first Fibonacci numbers up to the nth is equal to the $($n $+2)-$nd Fibonacci number minus $1.$ That is Fi $+$ F$2+...+$ Fn $=$ Fn$+2-1=1.$ Show by mathematical induction that the above identity is true. $2.$ Construct an algorithm which calculates the Fibonacci