MHB Understanding R-1/R and its Equivalence

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The discussion clarifies the expression r-1/r! and its equivalence. It explains that r! represents the factorial of r, which is the product of all positive integers up to r. The correct interpretation of r-1/r! leads to the conclusion that it equals (r-1)/r! or can be expressed as 1/(r-1)! - 1/r!. Additionally, the forum emphasizes the importance of users sharing their progress when asking questions to facilitate better assistance. Overall, the thread focuses on mathematical clarification and community engagement.
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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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greg1313
 
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