let's say F(.) is denoting the sequence of Joe. Remember that F (0) = 0, F (1) = 1 & for n > 1, F(n) = F(n 1) + F(n 2).

Show that for each n N*,

F(i)^2 =F(n)F(n+1)

(please look at image to understand the equation)

i=1nF(i)2=F(n)F(n+1)