How to manipulate factorials

  • Thread starter shanepitts
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  • #1
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I have been practicing power series problems and a lot of them include factorials. To find out if they converge or not I'll often use the ratio test. However, I never quite understood how to cancel factorials when replacing the n with n+1. i.e. the textbook has an example problem that shows that

[(n+1)!]2 ⇒ (n+1)2 (n!)

How is this done?

Thank you in advance.
 

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  • #2
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I have been practicing power series problems and a lot of them include factorials. To find out if they converge or not I'll often use the ratio test. However, I never quite understood how to cancel factorials when replacing the n with n+1. i.e. the textbook has an example problem that shows that

[(n+1)!]2 ⇒ (n+1)2 (n!)
In your example, [(n+1)!]2 means [(n+1)!] * [(n+1)!], which would be (n + 1)2(n)2(n - 1)2 ... 3222.
shanepitts said:
How is this done?

Thank you in advance.
 
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  • #3
statdad
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Note that [itex] [(n+1)!]^2 \ne \big(n+1\big)^2 \big(n!\big) [/itex], so you will have difficulty reducing the left side to the right side. :)
 
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  • #4
Mentallic
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A slight typo, but it should be
[(n+1)!]2 ⇒ (n+1)2 (n!)2
[tex](n+1)! = (n+1)\times n![/tex]

Hence

[tex]\left[ (n+1)!\right]^2 = \left[ (n+1)\times n!\right]^2[/tex]
 
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  • #5
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In your example, [(n+1)!]2 means [(n+1)!] * [(n+1)!], which would be (n + 1)2(n)2(n - 1)2 ... 3222.
Thanks
 

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