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1969 AMC 12 Question 16

AMC12 · 1969 AMC 12

Question 16

When $(a-b)^n,$ $n\ge2,$ $ab\ne0,$ is expanded by the binomial theorem, it is found that, when $a=kb,$ where $k$ is a positive integer, the sum of the second and third terms is zero. Then $n$ equals:
  1. $\dfrac12k(k-1)$
  2. $\dfrac12k(k+1)$
  3. $2k-1$
  4. $2k$
  5. $2k+1$