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Two distinct, real infinite geometric se...

Two distinct, real infinite geometric series each have a sum of 1 and have the same second term. The third term of one of the series is `1/8`. If the second term of both the series can be written in the form `(sqrtm-n)/p` where m,n and p are positive integers and m is not divisible by the square of any prime, find the value of `100m + 10n + p`.

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