Problem #428

Segments
Public 09/23/17 6xp Programming 43.5%

Let fib(n) be nth 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 vN be the vector of f(i) values for i=1 to N. For example v3=[2, 2, 3]

Let TN be the sum of the elements of VN. 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 vN starting from A to D.

si=vN[i]/TN*|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 ti for i=1 to N starting from A to B.

Find the sum of ratios |AB|/ti 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.




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