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Calculus Level 3

\[\LARGE \frac{1-\frac{1}{8}+\frac{1}{27}-\frac{1}{64}+\frac{1}{125}-\frac{1}{216}+\cdots}{1+\frac{1}{8}+\frac{1}{27}+\frac{1}{64}+\frac{1}{125}+\frac{1}{216}+\cdots}\]

If the ratio above can be written as \(\Large \frac{a}{b}\) where \(\large a\) and \(\large b\) are coprime integers. Find \(\large a \times b\).

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