6. Compare the numbers

$$
\left(1+\frac{1}{1755}\right)\left(1+\frac{1}{1756}\right) \ldots\left(1+\frac{1}{2015}\right) \text { and } \sqrt{\frac{8}{7}}
$$

Indicate in the answer «1» if the first number is greater; «2», if the second number is greater; «0», if the numbers are equal.
Answer: The first one is greater.

Solution: Convert each parenthesis on the left to a common denominator, then use the inequality $\frac{n \cdot n}{(n-1)(n+1)}>1$. Then we get that the square of the first number is greater than $\frac{2015}{1755}=\frac{31}{27}>\frac{8}{7}$.