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The sequence S is defined as Sn = (n + 1)!

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The sequence S is defined as Sn = (n + 1)!  [#permalink]

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New post 27 Dec 2014, 16:29
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  35% (medium)

Question Stats:

68% (01:56) correct 32% (01:57) wrong based on 172 sessions

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The sequence S is defined as Sn = (n + 1)! for all integers n >= 1. For example, S3 = 4! = (4)(3)(2)(1). Which of the following is equivalent to the difference between S100 and S99?

A) 101!
B) 100!
C) \(99^2 (98!)\)
D) \(100^2 (99!)\)
E) \((100!)^2\)
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The sequence S is defined as Sn = (n + 1)!  [#permalink]

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New post 27 Dec 2014, 17:31
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Hi pate13,

This question requires that you use a math rule that you probably already know AND that you convert your answer to match the format given in the answer choices.

According to this Symbolism question, we're asked to figure out S100 - S99. According to the description of the symbol in the question, we're asked to figure out:

101! - 100!

Both these terms have something in common: 100! so we can factor that out of each piece...

101! - 100!
100!(101 - 1)

Simplifying the parentheses, we get...

100!(100)

Unfortunately, THAT answer isn't listed. We've done the math correctly though, so all we can do is try to convert "our" answer into the format that appears in the answer choices...

100! = (100)(99!) so our answer can be rewritten as...

(100)(99!)(100)

Or....

(100^2)(99!)

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Re: The sequence S is defined as Sn = (n + 1)!  [#permalink]

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New post 27 Dec 2014, 19:24
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pate13 wrote:
The sequence S is defined as Sn = (n + 1)! for all integers n >= 1. For example, S3 = 4! = (4)(3)(2)(1). Which of the following is equivalent to the difference between S100 and S99?

A) 101!
B) 100!
C) \(99^2 (98!)\)
D) \(100^2 (99!)\)
E) \((100!)^2\)



S100 = 101!
S99 = 100!

S100-S99 = 101!-100!
= 101 * 100 ! - 1 * 100!
=100 * 100!
= 100 * 100(99!)
= 100^2 99!
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Re: The sequence S is defined as Sn = (n + 1)!  [#permalink]

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New post 11 Apr 2019, 17:32
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Re: The sequence S is defined as Sn = (n + 1)!   [#permalink] 11 Apr 2019, 17:32
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