Question

помогите мне с факториалами:2k!/(2k+1)! и 1/(k-1)!-1/k!

Answer 1

$1)~\,\dfrac{(2k)!}{\left(2k+1\right)!}=\dfrac{(2k)!}{\left(2k+1\right)(2k)!}=\dfrac{1}{2k+1}\bigskip\\2)~\,\dfrac{1}{\left(k-1\right)!}-\dfrac{1}{k!}=\dfrac{1}{\left(k-1\right)!}-\dfrac{1}{k\left(k-1\right)!}=\dfrac{k-1}{k\left(k-1\right)!}=\dfrac{\left(k-1\right)}{k\left(k-1\right)\left(k-2\right)!}=\medskip\\=\dfrac{1}{k\left(k-2\right)!}$