2. 外语
  3. If kSn is defined to be the product of (n + k)(n - k + 1) for all positive integers k and n, which of the following expressions

If kSn is defined to be the product of (n + k)(n - k + 1) for all positive integers k and n, which of the following expressions

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问题 If kSn is defined to be the product of (n + k)(n - k + 1) for all positive integers k and n, which of the following expressions represents k + 1Sn+1 +1?
选项 A、(n + k)(n-k + 2)
B、(n + k)(n-k + 3)
C、(n + k+1)(n-k + 2)
D、(n + k + 2)(n-k+1)
E、(n + k + 2)(n - k + 3)
答案D
解析 Substituting n + 1 for n and k + 1 for k in the definition gives k+1Sn+1 = (n + 1 + k+1)(n + 1-(k+1) + 1)= (n + k + 2)(n-k+1).
The correct answer is D.
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