1985 AJHSME Problem 9: Difference between revisions
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)}\ \..." |
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<math>\text{(A)}\ \frac {1}{10} \qquad \text{(B)}\ \frac {1}{9} \qquad \text{(C)}\ \frac {1}{2} \qquad \text{(D)}\ \frac {10}{11} \qquad \text{(E)}\ \frac {11}{2}</math> | <math>\text{(A)}\ \frac {1}{10} \qquad \text{(B)}\ \frac {1}{9} \qquad \text{(C)}\ \frac {1}{2} \qquad \text{(D)}\ \frac {10}{11} \qquad \text{(E)}\ \frac {11}{2}</math> | ||
== In-depth Solution by Boundless Brain!== | |||
https://youtu.be/yBrLXnjasgg | |||
== Solution == | == Solution == | ||
Revision as of 22:50, 29 June 2023
Problem
The product of the 9 factors 
In-depth Solution by Boundless Brain!
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: 
