## Problem of the Day #104: Sum Some Sums
*July 1, 2011*

*Posted by Saketh in : potd , trackback*

Evaluate

$$

\displaystyle\sum\limits_{a=1}^{10000} \;\;\;

\displaystyle\sum\limits_{b=a+3}^{10000} \;\;\;

\displaystyle\sum\limits_{c=b+3}^{10000} \;\;\;

\displaystyle\sum\limits_{d=c+3}^{10000} \;\;\;

\displaystyle\sum\limits_{e=d+3}^{10000} \;\;\;

\displaystyle\sum\limits_{f=e+3}^{10000} \;\;\;

1

$$

You may use a four-function calculator.

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