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$a_1+a_2+a_3+ ...$ is an infinite geometric series whose sum is $3$. Replacing each of the terms of the series by their squares results in a series whose sum is the same. Replacing each of the terms of the series by their cubes results in a series whose sum can be expressed by $\frac ab$ where $a$ and $b$ are co-pime positive integers. What is the value of $a+b$?

Source: BdMO

Algebra

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