56. Упростить: 1) $(n+3)!/(n+1)!$; 2) $(n+2)!/(n-1)!$; 3) $(1/(n+1)!+1/n!)\cdot n!$; 4) $(1/n!-1/(n+1)!)\cdot n!$; 5) $(1/n!-1/(n+2)!)\cdot(n+1)!$; 6) $(1/(n+2)!+1/n!)\cdot(n+1)!$.

Question

Вопрос: $Фото задания: 56. Упростить: 1) $(n+3)!/(n+1)!$; 2) $(n+2)!/(n-1)!$; 3) $(1/(n+1)!+1/n!)\cdot n!$; 4) $(1/n!-1/(n+1)!)\cdot n!$; 5)…$ Фото задания

56. Упростить: 1) $(n+3)!/(n+1)!$; 2) $(n+2)!/(n-1)!$; 3) $(1/(n+1)!+1/n!)\cdot n!$; 4) $(1/n!-1/(n+1)!)\cdot n!$; 5) $(1/n!-1/(n+2)!)\cdot(n+1)!$; 6) $(1/(n+2)!+1/n!)\cdot(n+1)!$.

Accepted Answer

$(n+3)!/(n+1)!=(n+3)(n+2)$.
$(n+2)!/(n-1)!=n(n+1)(n+2)$.
$(1/(n+1)!+1/n!)n!=1/(n+1)+1=(n+2)/(n+1)$.
$(1/n!-1/(n+1)!)n!=1-1/(n+1)=n/(n+1)$.
$(1/n!-1/(n+2)!)(n+1)!=n+1-1/(n+2)$.
$(1/(n+2)!+1/n!)(n+1)!=(n+1)+1/(n+2)$.

56. Упростить: 1) \((n+3)!/(n+1)!\); 2) \((n+2)!/(n-1)!\); 3) \((1/(n+1)!+1/n!)\cdot n!\); 4) \((1/n!-1/(n+1)!)\cdot n!\); 5) \((1/n!-1/(n+2)!)\cdot(n+1)!\); 6) \((1/(n+2)!+1/n!)\cdot(n+1)!\).

Ответ: