7.2. Find the value of the expression (1+1/2)(1+1/3)...(1+1/2012).
7.2. Answer: $\frac{2013}{2}=1006.5$

Perform the operation in each parenthesis:

$\left(1+\frac{1}{2}\right)\left(1+\frac{1}{3}\right) \ldots\left(1+\frac{1}{2012}\right)=\frac{3}{2} * \frac{4}{3} * \frac{5}{4} * \ldots * \frac{2012}{2011} * \frac{2013}{2012}$.

Notice that the numerator of each fraction coincides with the denominator of the next one, so they can be canceled out. The only ones that remain uncancelled are the denominator of the first fraction (it has no preceding fraction) and the numerator of the last fraction (it has no subsequent fraction). Thus, the product is $\frac{2013}{2}=1006.5$.

## Comments on Evaluation.

Only the answer is given without calculations or an unjustified pattern is used: 1 point. Correct logic, but an arithmetic error in calculations: 5 points.

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