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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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