Day 18: Splitting an Enormous Cake

Algebra Level 4

A mathematician has an enormous cake and many friends with whom to share it.

First, she gives a quarter of the cake to the first friend.

She then gives a fifth of the remaining cake to the next friend. She then gives a sixth of the now remaining cake to the next friend. This process continues until she gives a hundredth of the remaining cake to the last friend.

She finally takes the portion that is left over for herself.

What percentage of the original cake does she have?


This problem is part of the Advent Calendar 2015.
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