All get Equal Share

Algebra Level pending

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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