Understanding R-1/R and its Equivalence

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The discussion clarifies the mathematical expression r-1/r! and its equivalence. It establishes that r-1/r! can be expressed as (r-1)/r! and simplifies to 1/(r-1)! - 1/r!. The conversation emphasizes the importance of correctly interpreting factorial notation and provides a clear breakdown of the relationships between these expressions. Additionally, the forum encourages users to share their progress when seeking help to facilitate better assistance.

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Harry2
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Hey,
What is r-1/r! And sow it is equal to 1/(r-1) -1/r!
Thanks in advance.
 
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Harry said:
What is r-1/r!
$r!$ is called the factorial of $r$ and is equal to $1\cdot2\cdot3\cdot\ldots\cdot(r-1)\cdot r$.

Harry said:
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.
 
Hello Harry and welcome to MHB! :D

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