单选题 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?

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)

【正确答案】 D

【答案解析】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.