题目信息
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 ?
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)
参考答案及共享解析
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已选答案：
正确答案：
D:(n + k + 2)(n – k + 1)
Algebra Substitution; Simplifying algebraic expressions
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.
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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