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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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Joined: 04 Sep 2017
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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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21 Sep 2019, 05:20
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Question Stats:

72% (01:30) correct 28% (02:02) wrong based on 131 sessions

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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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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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Joined: 02 Sep 2009
Posts: 59125
Re: If kSn is defined to be the product of (n + k)(n – k + 1) for all posi  [#permalink]

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23 Sep 2019, 00:46
1
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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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

Posted from my mobile device
Math Expert
Joined: 02 Sep 2009
Posts: 59125
Re: If kSn is defined to be the product of (n + k)(n – k + 1) for all posi  [#permalink]

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23 Sep 2019, 02:19
1
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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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)

PS79302.01
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Joined: 12 Sep 2015
Posts: 4065
If kSn is defined to be the product of (n + k)(n – k + 1) for all posi  [#permalink]

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14 Oct 2019, 14:15
1
Top Contributor
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)

Cheers,
Brent
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If kSn is defined to be the product of (n + k)(n – k + 1) for all posi   [#permalink] 14 Oct 2019, 14:15
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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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