gmatt1476 wrote:
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 + 1)S(n + 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)
PS79302.01
Note that this question is a defined function question, where the letter S simply defines a relationship between two variables k and n, and the formula that relates them is (n + k)(n - k + 1).
Here is a simple example of this defined function kSn. Let’s calculate 3S5. This means that k = 3 and n = 5. So we have:
(5 + 3)(5 - 3 + 1)
We won’t actually calculate the numerical example, as this was simply an illustration of how to use the formula.
Now, let’s look at (k + 1)S(n + 1). We see that now, wherever there is a “k” in the formula, we will substitute (k + 1), and wherever there is an “n” in the formula, we will substitute (n + 1).
(k + 1)S(n + 1)
The formula is: (n + k)(n - k + 1), so our substitutions are:
(n + 1 + k + 1) x [(n + 1 - (k + 1) + 1]
(n + k + 2) x (n - k + 1)
Answer: D
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