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1−(31)13+(42)19−(53)127+… \large 1 - \dbinom31 \frac13 + \dbinom42\frac19 -\dbinom53\frac1{27}+\ldots 1−(13)31+(24)91−(35)271+…
If the above summation is equal to SSS, evaluate 100×S3100\times \sqrt[3]S100×3S.
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