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Which of the following is equal to n!*(n+1)!?

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Which of the following is equal to n!*(n+1)!?  [#permalink]

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New post 23 May 2017, 01:27
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Which of the following is equal to n!*(n+1)!?

A. \((n!)^2\)
B. \((n+1)!^2\)
C. \(n!^3(n+1)!^2\)
D. \(n!^3(n+1)\)
E. \(n!^2(n+1)\)

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Re: Which of the following is equal to n!*(n+1)!?  [#permalink]

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New post 23 May 2017, 04:09
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MathRevolution wrote:
Which of the following is equal to n!*(n+1)!?

A. \((n!)^2\)
B. \((n+1)!^2\)
C. \(n!^3(n+1)!^2\)
D. \(n!^3(n+1)\)
E. \(n!^2(n+1)\)


n!*(n+1)!
Let n be 2.
2!*(2+1)! = 2! * 3! = (2 *1 )(3 * 2* 1) = \((2!)^2\)(2+1)
\(n!^2\)(n+1)
Answer E...


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Re: Which of the following is equal to n!*(n+1)!?  [#permalink]

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New post 23 May 2017, 04:42
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MathRevolution wrote:
Which of the following is equal to (n!)(n+1)!?

A. \((n!)^2\)
B. \((n+1)!^2\)
C. \(n!^3(n+1)!^2\)
D. \(n!^3(n+1)\)
E. \(n!^2(n+1)\)


Notice that (n+1)(n!) = (n+1)!
Why is this?
Well if we expand n! to be (n)(n-1)(n-2)....(3)(2)(1) we can see why.
We get: (n+1)(n!) = (n+1)(n)(n-1)(n-2)....(3)(2)(1)
= (n+1)!


So, (n!)(n+1)! = (n!)(n+1)(n!)
= (n!)² (n+1)

Answer:
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Re: Which of the following is equal to n!*(n+1)!?  [#permalink]

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New post 23 May 2017, 07:40
MathRevolution wrote:
Which of the following is equal to n!*(n+1)!?

A. \((n!)^2\)
B. \((n+1)!^2\)
C. \(n!^3(n+1)!^2\)
D. \(n!^3(n+1)\)
E. \(n!^2(n+1)\)


\(n!(n+1)! = n! \times n! \times (n+1) = (n!)^2 \times (n+1)\)

The answer is E
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Re: Which of the following is equal to n!*(n+1)!?  [#permalink]

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New post 25 May 2017, 00:19
==> You get n!*(n+1)!=n!*(n+1)n!=(n!)^2(n+1). The answer is E.

Answer: E
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Re: Which of the following is equal to n!*(n+1)!?  [#permalink]

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