# Pairs upstairs

Calculus Level 5

Calculate

$\displaystyle\ln\left(\sum\limits_{\gamma_1\in\{-1,1\}}\ldots\sum\limits_{\gamma_{2014}\in\{-1,1\}}e^{\gamma_1\gamma_2}e^{\gamma_2\gamma_3}\ldots e^{\gamma_{2013}\gamma_{2014}}\right).$

Note: This kind of summation has applications in the statistical mechanics of magnets and simple models of neural networks.

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