Difference between revisions of "1984 AJHSME Problem 9"
Coolmath34 (talk | contribs) (Created page with "== Problem == The product of the 9 factors <math>\Big(1 - \frac12\Big)\Big(1 - \frac13\Big)\Big(1 - \frac14\Big)\cdots\Big(1 - \frac {1}{10}\Big) =</math> <math>\text{(A)}\ \...") |
Coolmath34 (talk | contribs) (→Problem) |
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== Solution == | == Solution == | ||
This product simplifies to: | This product simplifies to: | ||
<cmath>\frac{1}{2} \cdot \frac{2}{3} \dots \frac{9}{10}.</cmath> | <cmath>\frac{1}{2} \cdot \frac{2}{3} \dots \frac{9}{10}.</cmath> | ||
Numerators and denominators cancel to yield the answer: <math>\boxed{\text{(A)} \frac{1}{10}}.</math> | Numerators and denominators cancel to yield the answer: <math>\boxed{\text{(A)} \frac{1}{10}}.</math> | ||
Revision as of 20:43, 31 January 2021
Solution
This product simplifies to:
![\[\frac{1}{2} \cdot \frac{2}{3} \dots \frac{9}{10}.\]](http://latex.artofproblemsolving.com/c/d/f/cdf3e4229337b6e0cb5e4e4d010c70f59ef5a685.png)
Numerators and denominators cancel to yield the answer: 
