Question

Запишите в виде дроби.1 / (k - 1)! - k / (k + 1)!Очень прошу, помогите!!!

Answer 1

$\frac{1}{(k-1)!}-\frac{k}{(k+1)!}=\\\\\frac{1}{(k-1)!}-\frac{k}{(k-1)!*k*(k+1)}=\\\\\frac{1}{(k-1)!}-\frac{1}{(k-1)!(k+1)}=\\\\\frac{1*(k+1)-1}{(k-1)!*(k+1)}=\\\\\frac{k+1-1}{(k-1)!(k+1)}=\\\\\frac{k}{(k-1)!(k+1)}$
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(или дальше)
$=\frac{k*k}{(k-1)!*k(k+1)}=\frac{k^2}{(k+1)!}$