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The value of $$\left(1+\frac{1}{9}\right)\left(1+\frac{1}{8}\right)\left(1+\frac{1}{7}\right)\left(1+\frac{1}{6}\right)\left(1+\frac{1}{5}\right)\left(1+\frac{1}{4}\right)\left(1+\frac{1}{3}\right)\left(1+\frac{1}{2}\right)$$ is
Correct Answer: 5
Each factor can be written as $$\frac{10}{9} \times \frac{9}{8} \times \frac{8}{7} \times \frac{7}{6} \times \frac{6}{5} \times \frac{5}{4} \times \frac{4}{3} \times \frac{3}{2}$$, and every term in the middle cancels with the next, leaving $$\frac{10}{2} = 5$$.
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