Difference between revisions of "1992 AJHSME Problems/Problem 25"
(Created page with 'Model the amount left in the container as follows: After the first pour 1/2 remains, after the second 1/2*2/3 remains, etc This becomes the product 1/2*2/3*3/4...9/10 Note tha…') |
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Revision as of 16:03, 3 April 2011
Model the amount left in the container as follows:
After the first pour 1/2 remains, after the second 1/2*2/3 remains, etc
This becomes the product 1/2*2/3*3/4...9/10
Note that the terms cancel out leaving 1/10
Now all that remains is to count the number of terms, as the denominators form an arithmetic sequence with a common difference of 1 and endpoints (2,10) there are 10-2+1=9 terms
