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((n-1)!+n!+(n+1)!)/n!

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GeminiHeat
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((n-1)!+n!+(n+1)!)/n! [#permalink] New post   15 Nov 2021, 06:27
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(n−1)!+n!+(n+1)!n!

Which of the following values of n will result between 16 and 17 for the equation?

A. 14
B. 15
C. 16
D. 17
E. 18
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A
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GreenlightTestPrep
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((n-1)!+n!+(n+1)!)/n! [#permalink] New post   15 Nov 2021, 06:58
GeminiHeat wrote:
(n−1)!+n!+(n+1)!n!

Which of the following values of n will result between 16 and 17 for the equation?

A. 14
B. 15
C. 16
D. 17
E. 18


Useful fraction property: a+b+cd=ad+bd+cd

Apply the property to get: (n−1)!+n!+(n+1)!n!=(n−1)!n!+n!n!+(n+1)!n!

=1n+1+(n+1)

=n+2+1n

From the answer choices, we can see that the value of n must be an integer from 14 to 18 inclusive, which means the fraction 1n must be between 0 and 1.

This means the expression n+2+1n will be between 16 and 17 when n=14

Answer: A
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((n-1)!+n!+(n+1)!)/n! [#permalink] New post   17 Nov 2021, 01:35
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(n−1)!+n!+(n+1)!n!=(n−1)!n!+n!n!+(n+1)!n!=(n−1)!n∗(n−1)!+1+(n+1)∗n!n!=1n+1+(n+1)=n+2+1n

Since all options are greater than 1, 0<1n<1

We only need to check the term (n+2) to find the answer.

Except for 14 all other options go above 17.

Hence, Answer is A
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Re: ((n-1)!+n!+(n+1)!)/n! [#permalink] New post   09 Sep 2023, 10:37
Hello from the GRE Prep Club BumpBot!

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Re: ((n-1)!+n!+(n+1)!)/n! [#permalink]
09 Sep 2023, 10:37
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