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1986 AMC 12 Question 9

AMC12 · 1986 AMC 12

Question 9

The product $$
\begin{aligned} &\left(1-\frac1{2^2}\right) \left(1-\frac1{3^2}\right)\\ &\quad{}\cdots \left(1-\frac1{9^2}\right) \left(1-\frac1{10^2}\right) \end{aligned}
$$ equals
  1. $\frac5{12}$
  2. $\frac12$
  3. $\frac{11}{20}$
  4. $\frac23$
  5. $\frac7{10}$