1. Read "Fibonacci sequence" in the appendices. 2. Show that the sum of the squares of the first n Fibonacci numbers is given by the formula F_{1}^{2}+F_{2}^{2}+\ldots+F_{n}^{2}=F_{n} F_{n+1} \text {

Hint: } F_{n}^{2}=F_{n}\left(F_{n+1}-F_{n-1}\right)=F_{n} F_{n+1}-F_{n} F_{n-1} 3. It can be established that each positive integer equals to a sum of Fibonacci numbers,none taken more than once. For example, 5 = F3+ F4, 6 = F1+ F3 + F4, 7 =F1 + F2+ F3 + F4. Write the integers 50 and 75 in this manner.