1976 AHSME Problems/Problem 21
Revision as of 19:54, 19 July 2021 by Jiang147369 (talk | contribs) (Created page with "== Problem 21 == What is the smallest positive odd integer <math>n</math> such that the product <math>2^{1/7}2^{3/7}\cdots2^{(2n+1)/7}</math> is greater than <math>1000</math...")
Problem 21
What is the smallest positive odd integer such that the product is greater than ? (In the product the denominators of the exponents are all sevens, and the numerators are the successive odd integers from to .)
Solution
Combine the terms in the product to get .
The exponent can be simplified to
We want this inequality to be true with the smallest positive odd integer value of :
Now, let's test the answer choices. For , we have . For , we have .
So our answer is . ~jiang147369
See Also
1976 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 20 |
Followed by Problem 22 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.