Question

R!/(R-1)! =R
How ¿??

Answer 1

Answer:

$\displaystyle \frac{\mathrm{R}!}{\left(\mathrm{R}-1\right)!}=\mathrm{R}\quad :\quad \mathrm{True\:for\:all}\:\mathrm{R}$

Step-by-step explanation:

$\dfrac{\mathrm{R}!}{\left(\mathrm{R}-1\right)!}=\mathrm{R}$

$\black{\mathrm{Simplify\:}\dfrac{\mathrm{R}!}{\left(\mathrm{R}-1\right)!}:}$

$\dfrac{\mathrm{R}!}{\left(\mathrm{R}-1\right)!}$

$\gray{\mathrm{Cancel\:the\:factorials}:\quad \dfrac{n!}{\left(n-r\right)!}=n\cdot \left(n-1\right)\cdots \left(n-r+1\right),\:n>r}$

$\gray{\dfrac{\mathrm{R}!}{\left(\mathrm{R}-1\right)!}=\mathrm{R}}$

$=\mathrm{R}$

$\blue{\mathrm{Both\:sides\:are\:equal}}$

$\mathrm{True\:for\:all}\:\mathrm{R}$

Answer 2

Answer:

Step-by-step explanation:

take r=1

=1!(1-1)!

As the rule 0! = 1

1! =1

=1(0)!

=1(1)

1!(1-1)!=1

Hence proved R=R!(R-1)!