## Problem of the Day #113: Fibonacci Fun
*July 10, 2011*

*Posted by Sreenath in : potd , trackback*

The Fibonacci sequence is defined as $F_1=1,F_2=1$ and $F_n=F_{n-1}+F_{n-2}$. Compute the real part of $$\sum\limits_{k=1}^{999}\; ki^{\left(F_k\right)^2}$$ You may use a four-function calculator.

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