Classical Studies 2302A/B Lecture : Democracy at Athens

9. The Fibonacci squence F is defined by Fi 1, F n 2. Thus, F2 F1 1 1 2 1 1, and F n-+1 Fn n-1 for

Consider the functions fn : [0,1] right arrow R. fn(x) = nx''(1 - x) a. Find f(x)= Iim n right arrow infinity fn(x) b. Does fn right arrow f uniformly on [0, 1]? c. Does integrate 0 1 fn(x) dx converge to integrate 0 1 f(x)dx?