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In the given series we can easily observe that the denominator of the first term is equal to the numerator of the succeeding term. Hence we can easily cancel them out or in other words the numerator of the second term is exactly divisible by the denominator of the first term. If we keep on performing this operation for all the terms in the end we will be left with 2/99 × 99/100 which will give us final answer as 2/100 which can be further simplified to 1/50 or 0.02.
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