Đáp án:
Giải thích các bước giải:
S=1.4+2.5+3.6+4.7+....+n.(n+3)
$S=1.(2+2)+2.(3+2)+3.(4+2)+...+n.[(n+1)+2]$
$S=1.2+2.3+3.4+....+n.(n+1)+(1.2+2.2+3.2+....+n.2)$
Đặt $A=1.2+2.3+3.4+....+n.(n+1)$
$3A=1.2.3+2.3.(4-1)+....+n.(n+1).[(n+2)-(n-1)$
$3A=1.2.3+2.3.4-1.2.3+....+n.(n+1).(n+2)-(n-1).n.(n+1)$
$3A=n.(n+1).(n+2)$
$A=[n.(n+1).(n+2)]:3$
$S=[n.(n+1).(n+2)]:3 + 2.(1+2+3+...+n)$
$S=[n.(n+1).(n+2)]:3 + 2.n.(n+1):2$
$S=n.(n+1).(n+2):3 + n.(n+1)$
$S=n.(n+1).[(n+2):3+1)$
