I am wondering what is domain of this expression:
$\dfrac1{(n+2)!}$
It seems for me like it has to be $\;n+2\geqslant0\;$ and then has to be $\;n\geqslant -2.$
But we can write the factorial expression like this: $(n+2)(n+1)!$
And now when we will install number $-2$ it will be: $\;0\cdot(-1)! = 0\;$ because everything multiplied by $0$ is $0.$ So in the interval can’t be the number $-2.$
Can someone help me if someone understand me what I mean? Thanks!
By definition $0!=1$. So we can write $ (n+2)!=(n+2)(n+1)!$ only if $n+2>0$