Difference between revisions of "1968 AHSME Problems/Problem 27"
(Created page with "== Problem == Let <math>S_n=1-2+3-4+\cdots +(-1)^{n-1}n</math>, where <math>n=1,2,\cdots</math>. Then <math>S_{17}+S_{33}+S_{50}</math> equals: <math>\text{(A) } 0\quad \text{(...") |
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== Solution == | == Solution == | ||
| − | <math>\fbox{}</math> | + | If <math>n</math> is even, <math>S_{n}</math> is negative <math>n/2</math>. If <math>n</math> is odd, then <math>S_{n}</math> is <math>(n+1)/2</math>. |
| + | (These can be found using simple calculations.) | ||
| + | Therefore, we know <math>S_{17}+S_{33}+S_{50}</math> =<math>9+17-25</math>, which is <math>\fbox{B}</math>. | ||
| + | |||
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| + | Solution By FrostFox | ||
== See also == | == See also == | ||
| − | {{AHSME box|year=1968|num-b=26|num-a=28}} | + | {{AHSME 35p box|year=1968|num-b=26|num-a=28}} |
[[Category: Intermediate Algebra Problems]] | [[Category: Intermediate Algebra Problems]] | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Latest revision as of 00:53, 16 August 2023
Problem
Let 
, where 
. Then 
equals:
Solution
If 
is even, 
is negative 
. If is odd, then is 
.
(These can be found using simple calculations.)
Therefore, we know =
, which is 
.
Solution By FrostFox
See also
| 1968 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 26 |
Followed by Problem 28 | |
| 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 • 31 • 32 • 33 • 34 • 35 | ||
| All AHSME Problems and Solutions | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
