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Problem #40

Kyle's Mysterious Sequences

For a given integer n, Consider the following functions G(n) and F(n)

G(n) = \sqrt{F(n) - \frac{(n-1)^2}{n^2}F(n-1) + \frac{1}{n^2}}

F(n) = 8 + \frac{(n-2)^2}{n^2}F(n-2)

F(1) = F(2) = 8

Now consider the sequences

Y(n) = \sum{x} | x < n, n \mod x=0
Z(n) = Z(n-1) + Y(n)
Z(0) = Z(1) = 0

Find the value of Z(\frac{1}{(G (1000000000)-2)})

Contributed by Nitish Sharma

Solved by 79 users

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