Sums of Sums of Sums of

Algebra Level 5

Let \[N=\underbrace{\displaystyle\sum^{2014}_{a_1=1}\sum^{a_1}_{a_2=1}\cdots \sum^{a_{2013}}_{a_{2014}=1}}_{2014\text{ sums}}1\]

How many zeroes to the right of the right-most non-zero decimal digit are in \(N\)?

\(\text{Details and Assumptions}\)

  • If \(N=10080000\), then the answer would be \(4\).
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