- #1

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## Homework Statement

Show that n/(n+1)!=(1/n)-(1/(n+1)!)

I am totally lost on the algebraic steps taken to come to this conclusion. It is for an

Infinite series.

Thanks

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- Thread starter danerape
- Start date

- #1

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Show that n/(n+1)!=(1/n)-(1/(n+1)!)

I am totally lost on the algebraic steps taken to come to this conclusion. It is for an

Infinite series.

Thanks

- #2

vela

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[tex]\frac{n}{(n+1)!} = \frac{3}{4!} = \frac{3}{24} = \frac{1}{8}[/tex]but

[tex]\frac{1}{n}-\frac{1}{(n+1)!} = \frac{1}{3}-\frac{1}{24} = \frac{8}{24}-\frac{1}{24} = \frac{7}{24}[/tex]

- #3

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

- #4

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Wow, sorry. I meant n/(n+1)!=1/n! - 1/(n+1)!

- #5

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It's easy to prove. In the LHS write n=(n+1)-1.

- #6

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Dane

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