k! * (k + 1) == (k + 1)!; How?

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syntaxerror
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k! * (k + 1) == (k + 1)!; How?

Postby syntaxerror » Wed Jul 24, 2013 6:03 pm

k!(k + 1) = (k + 1)!

How does the left simplify to the expression on the right?

(I understand what factorial is, and I can find rules for multiplying two factorials, but I don't have any rules for multiplying a sum by a factorial.)

jg.allinsymbols
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Re: k! * (k + 1) == (k + 1)!; How?

Postby jg.allinsymbols » Thu Jul 25, 2013 2:31 am

syntaxerror wrote:k!(k + 1) = (k + 1)!

How does the left simplify to the expression on the right?

(I understand what factorial is, and I can find rules for multiplying two factorials, but I don't have any rules for multiplying a sum by a factorial.)


k!(k+1)=(k+1)*k!
=(k+1)*(k)(k-1)(k-2)...(3)(2)(1)
=(k+1)!


Look carefully that k=(k+1)-1


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