An old and crafty mathematician had \(n\) children, not all of the same sex, none of whom were of the same age. His will was short and sweet. It said :

"My property should be distributed among my children, starting from the eldest to youngest. The \(i\)-th child gets \($1000\times i+ 10\% \mbox{ of what that remains}\)."

However, in spite of the apparent inequality in distribution, everyone got an equal share. If all the children gave \(0.5 \%\) of their inheritance as tax. What was the total amount of tax collected from the \(n\) children?

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