MHB Understanding R-1/R and its Equivalence

[Harry2]

Hey,
What is r-1/r! And sow it is equal to 1/(r-1) -1/r!
Thanks in advance.

 

[Evgeny.Makarov]

What is r-1/r!

$r!$ is called the factorial of $r$ and is equal to $1\cdot2\cdot3\cdot\ldots\cdot(r-1)\cdot r$.

And sow it is equal to 1/(r-1) -1/r!

It is not. If you mean $\dfrac{r-1}{r!}=(r-1)/r!$, then it is equal to $\dfrac{r}{r!}-\dfrac{1}{r!}=\dfrac{1}{(r-1)!}-\dfrac{1}{r!}$ because $\dfrac{r}{r!}=\dfrac{r}{1\dots\cdot(r-1)r}=\dfrac{1}{1\dots\cdot(r-1)}=\dfrac{1}{(r-1)!}$. If you mean $r-1/r!=r-\dfrac{1}{r!}$, then it can't be further simplified.

 

[Greg]

Hello Harry and welcome to MHB! :D

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Thanks,

greg1313