# Inspired by Otto...Funny back to the future

Number Theory Level 4

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

$(1 \cdot 1) + (1 \cdot 2) + (2 \cdot 3) + (3 \cdot 5) + \ldots + (f_{2012} \cdot f_{2013}) + (f_ {2013} \cdot f_{2014})$

If the value of the expression above equals $$f_n ^2$$, find the value of $$n$$.

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