- #1

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[(n+1)!]

^{2}⇒ (n+1)

^{2}(n!)

How is this done?

Thank you in advance.

- Thread starter shanepitts
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- #1

- 84

- 1

[(n+1)!]

How is this done?

Thank you in advance.

- #2

Mark44

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In your example, [(n+1)!]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!)

shanepitts said:How is this done?

Thank you in advance.

- #3

statdad

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- #4

Mentallic

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[tex](n+1)! = (n+1)\times n![/tex][(n+1)!]^{2}⇒ (n+1)^{2}(n!)^{2}

Hence

[tex]\left[ (n+1)!\right]^2 = \left[ (n+1)\times n!\right]^2[/tex]

- #5

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ThanksIn your example, [(n+1)!]^{2}means [(n+1)!] * [(n+1)!], which would be (n + 1)^{2}(n)^{2}(n - 1)^{2}... 3^{2}2^{2}.

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