Inspired by Otto...Funny back to the future

The Fibonacci sequence is defined with the recurrence relation fn=fn1+fn2f_{n} = f_{n-1} + f_{n-2} for n>2n>2 with initial terms f1=1f_1 = 1, f2=1f_2 = 1.

(11)+(12)+(23)+(35)++(f2012f2013)+(f2013f2014) (1 \cdot 1) + (1 \cdot 2) + (2 \cdot 3) + (3 \cdot 5) + \ldots + (f_{2012} \cdot f_{2013}) + (f_ {2013} \cdot f_{2014})

If the value of the expression above equals fn2 f_n ^2 , find the value of nn.

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