Segments

Let fib(n) be n_th Fibonacci number. fib(1)=1, fib(2)=1 and fib(n) = fib(n-1) + fib(n-2) for n>2. Let f(n)=1+(fib(n)%5) Let v_N be the vector of f(i) values for i=1 to N. For example v₃=[2, 2, 3] Let T_N be the sum of the elements of V_N. For example T₃=7 Consider an ABC triangle and a D point that bisects BC side: |BD|=|CD| Draw the AD segment and assume N-1 points on it that further creates N segments such that the lengths of these subsegments are proportional to the elements of v_N starting from A to D. s_i=v_N[i]/T_N*|AD| for i=1 to N Now draw the line segments from C to AB that cross these N-1 points on AD segment. So now we have N subsegments on AB side as well. Let the lengths of these subsegments on the AB side be given as t_i for i=1 to N starting from A to B. Find the sum of ratios |AB|/t_i for i=1 to N where N = 1919. Answer format: p/q (reduced fraction) You are given that the answer = 251/21 for N = 3.