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1968 AMC 12 Question 17

AMC12 · 1968 AMC 12

Question 17

Let $f(n)=\dfrac{x_1+x_2+\cdots+x_n}{n},$ where $n$ is a positive integer. If $x_k=(-1)^k,$ $k=1,$ $2,$ $\ldots,$ $n,$ the set of possible values of $f(n)$ is:
  1. $\{0\}$
  2. $\left\{\dfrac1n\right\}$
  3. $\left\{0,-\dfrac1n\right\}$
  4. $\left\{0,\dfrac1n\right\}$
  5. $\left\{1,\dfrac1n\right\}$