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If kSn is defined to be the product of (n + k)(n – k + 1) for all posi

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If kSn is defined to be the product of (n + k)(n – k + 1) for all posi  [#permalink]

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New post 21 Sep 2019, 05:20
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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)


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Re: If kSn is defined to be the product of (n + k)(n – k + 1) for all posi  [#permalink]

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New post 21 Sep 2019, 06:46
gmatt1476 wrote:
If \(kS_n\) 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 \(k + 1S_n + 1\) ?

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


\(k + 1S_n + 1\) can be interpreted in more than 1 way: (k + 1)\(S_n\) + 1 or \((k + 1)S_{n + 1}\) or k + \(1S_n\) + 1
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Re: If kSn is defined to be the product of (n + k)(n – k + 1) for all posi  [#permalink]

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New post 23 Sep 2019, 00:46
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Dillesh4096 wrote:
gmatt1476 wrote:
If \(kS_n\) 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 \(k + 1S_n + 1\) ?

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


\(k + 1S_n + 1\) can be interpreted in more than 1 way: (k + 1)\(S_n\) + 1 or \((k + 1)S_{n + 1}\) or k + \(1S_n\) + 1


There is not brackets there, so it's k + \(1S_n\) + 1
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Re: If kSn is defined to be the product of (n + k)(n – k + 1) for all posi  [#permalink]

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New post 23 Sep 2019, 02:00
1
Bunuel wrote:
Dillesh4096 wrote:
gmatt1476 wrote:
If \(kS_n\) 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 \(k + 1S_n + 1\) ?

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


\(k + 1S_n + 1\) can be interpreted in more than 1 way: (k + 1)\(S_n\) + 1 or \((k + 1)S_{n + 1}\) or k + \(1S_n\) + 1


There is not brackets there, so it's k + \(1S_n\) + 1


But that gives k + \(1S_n\) + 1 as
k + (n + 1)(n - 1 + 1) + 1
= k + (n + 1)*n + 1
= n^2 + n + k + 1
Which is NOT equal to D.

Only if I take it as \((k + 1)S_{n + 1}\)
= (n + 1 + k + 1)((n + 1) - (k + 1) + 1)
= (n + k + 2)(n - k + 1)
Which gives me option D.

So, in my opinion the representation in the question is not clear

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Re: If kSn is defined to be the product of (n + k)(n – k + 1) for all posi  [#permalink]

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New post 23 Sep 2019, 02:19
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Dillesh4096 wrote:
Bunuel wrote:
Dillesh4096 wrote:

\(k + 1S_n + 1\) can be interpreted in more than 1 way: (k + 1)\(S_n\) + 1 or \((k + 1)S_{n + 1}\) or k + \(1S_n\) + 1


There is not brackets there, so it's k + \(1S_n\) + 1


But that gives k + \(1S_n\) + 1 as
k + (n + 1)(n - 1 + 1) + 1
= k + (n + 1)*n + 1
= n^2 + n + k + 1
Which is NOT equal to D.

Only if I take it as \((k + 1)S_{n + 1}\)
= (n + 1 + k + 1)((n + 1) - (k + 1) + 1)
= (n + k + 2)(n - k + 1)
Which gives me option D.

So, in my opinion the representation in the question is not clear

Posted from my mobile device


Dillesh4096 you are totally right. It's (k + 1)S(n + 1). Edited. By bad. Thank you.
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Re: If kSn is defined to be the product of (n + k)(n – k + 1) for all posi  [#permalink]

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New post 23 Sep 2019, 03:33
given function ; kSn = (n + k)(n – k + 1)
so for
(k + 1)S(n + 1)= (n+1+k+1)(n+1-k-1+1) ; (n + k + 2)(n – k + 1)
IMO D

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)


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If kSn is defined to be the product of (n + k)(n – k + 1) for all posi  [#permalink]

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New post 14 Oct 2019, 14:15
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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


GIVEN: kSn = (n + k)(nk + 1)

For example: 5S2 = (2 + 5)(25 + 1)
= (7)(-2)
= -14

And 7S3 = (3 + 7)(37 + 1)
= (10)(-3)
= -30

Now let's answer the question....
(k+1)S(n+1) = [(n+1) + (k+1)][(n+1)(k+1) + 1]
= (n + k + 2)(n - k + 1)

Answer: D

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Re: If kSn is defined to be the product of (n + k)(n – k + 1) for all posi  [#permalink]

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New post 15 Dec 2019, 14:39
Hi All,

We're told that kSn is defined to be the product of (n + k)(n - k + 1) for all positive integers k and n. We're asked for the value of (k + 1)S(n + 1). This is a "Symbolism" question (the prompt 'makes up' a math symbol, tells us how it 'works' and asks us to perform a calculation with it) and it can be approached in a couple of different ways, including by TESTing VALUES.

IF.... K = 2 and N = 3....
then we're asked to find the value of 3S4....

According to the given formula, that would be (4+3)(4 - 3 + 1) = (7)(2) = 14. So we're looking for an answer that equals 14 when K=2 and N=3. There's only one answer that matches...

Final Answer:

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Re: If kSn is defined to be the product of (n + k)(n – k + 1) for all posi  [#permalink]

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New post 23 Dec 2019, 18:23
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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Re: If kSn is defined to be the product of (n + k)(n – k + 1) for all posi   [#permalink] 23 Dec 2019, 18:23
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