1968 AHSME Problems/Problem 27

Problem

Let $S_n=1-2+3-4+\cdots +(-1)^{n-1}n$ , where $n=1,2,\cdots$ . Then $S_{17}+S_{33}+S_{50}$ equals:

$\text{(A) } 0\quad \text{(B) } 1\quad \text{(C) } 2\quad \text{(D) } -1\quad \text{(E) } -2$

Solution

If $n$ is even, $S_{n}$ is negative $n/2$ . If $n$ is odd, then $S_{n}$ is $(n+1)/2$ . (These can be found using simple calculations.) Therefore, we know $S_{17}+S_{33}+S_{50}$ = $9+17-25$ , which is $\fbox{B}$ .

Solution By FrostFox

1968 AHSME (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
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1968 AHSME Problems/Problem 27

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