IMC 2015/3

Consider the recurrence relation with initial values \( F(0) = 0, F(1) = \frac{3}{2} \) and \[ F(n) = \frac{5}{2} F(n-1) - F(n-2). \]

To 2 decimal places, evaluate \[ \sum_{n=0}^ \infty \frac{1}{ F(2 ^n ) } . \]

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