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Omni-MATH / 100 numbers 1, 1/2, 1/3, ..., 1/100 are written on the blackboard. One may delete two arbitrary numbers a and b among them and replace them by the number a+b+ab. After 99 such oper…

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problem

100100 numbers 11, 1/21/2, 1/31/3, ......, 1/1001/100 are written on the blackboard. One may delete two arbitrary numbers aa and bb among them and replace them by the number a+b+aba + b + ab. After 9999 such operations only one number is left. What is this final number? (D. Fomin, Leningrad)
Plain-text mathematical notation (without MathML)
100 numbers 1, 1/2, 1/3, ..., 1/100 are written on the blackboard. One may delete two arbitrary numbers a and b among them and replace them by the number a+b+ab. After 99 such operations only one number is left. What is this final number?

(D. Fomin, Leningrad)
Original LaTeX notation
$100$ numbers $1$, $1/2$, $1/3$, $...$, $1/100$ are written on the blackboard. One may delete two arbitrary numbers $a$ and $b$ among them and replace them by the number $a + b + ab$. After $99$ such operations only one number is left. What is this final number?

(D. Fomin, Leningrad)

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Source and history

task_id
59012036-2593-5a4b-aadf-5196cff60822
task_key
test--59012036-2593-5a4b-aadf-5196cff60822
task_revision_id
1
config / split
/ test

Official source

initial import