![\[\left(\frac{1\cdot3}{2\cdot2}\right)\left(\frac{2\cdot4}{3\cdot3}\right)\left(\frac{3\cdot5}{4\cdot4}\right)\cdots\left(\frac{97\cdot99}{98\cdot98}\right)\left(\frac{98\cdot100}{99\cdot99}\right)?\]](https://latex.artofproblemsolving.com/9/c/a/9ca55aef127eee6fc870173ae1b23e1abd56a02b.png)
We will try to see how many numbers repeat in both the numerator and denominator, and cross them out. We find that the bottom right of a parenthesis corresponds with the top left of the next consecutive parenthesis. The top right of a parenthesis corresponds with the bottom left of the next consecutive parenthesis.
We cross out all the numbers except for the leftmost and rightmost numbers. We get: (1 * 100)/(2 * 99) = 50/99, so the answer is B.
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