National and Regional Contests USA Contests MAA AMC AMC 12/AHSME 1986 AMC 12/AHSME 9 Series product Problem Statement The product ( 1 − 1 2 2 ) ( 1 − 1 3 2 ) … ( 1 − 1 9 2 ) ( 1 − 1 1 0 2 ) \left(1 - \frac{1}{2^{2}}\right)\left(1 - \frac{1}{3^{2}}\right)\ldots\left(1 - \frac{1}{9^{2}}\right)\left(1 - \frac{1}{10^{2}}\right) ( 1 − 2 2 1 ) ( 1 − 3 2 1 ) … ( 1 − 9 2 1 ) ( 1 − 1 0 2 1 ) < s p a n c l a s s = ′ l a t e x − b o l d ′ > ( A ) < / s p a n > 5 12 < s p a n c l a s s = ′ l a t e x − b o l d ′ > ( B ) < / s p a n > 1 2 < s p a n c l a s s = ′ l a t e x − b o l d ′ > ( C ) < / s p a n > 11 20 < s p a n c l a s s = ′ l a t e x − b o l d ′ > ( D ) < / s p a n > 2 3 < s p a n c l a s s = ′ l a t e x − b o l d ′ > ( E ) < / s p a n > 7 10 <span class='latex-bold'>(A)</span>\ \frac{5}{12}\qquad<span class='latex-bold'>(B)</span>\ \frac{1}{2}\qquad<span class='latex-bold'>(C)</span>\ \frac{11}{20}\qquad<span class='latex-bold'>(D)</span>\ \frac{2}{3}\qquad<span class='latex-bold'>(E)</span>\ \frac{7}{10} < s p an c l a ss = ′ l a t e x − b o l d ′ > ( A ) < / s p an > 12 5 < s p an c l a ss = ′ l a t e x − b o l d ′ > ( B ) < / s p an > 2 1 < s p an c l a ss = ′ l a t e x − b o l d ′ > ( C ) < / s p an > 20 11 < s p an c l a ss = ′ l a t e x − b o l d ′ > ( D ) < / s p an > 3 2 < s p an c l a ss = ′ l a t e x − b o l d ′ > ( E ) < / s p an > 10 7