2 câu trả lời
$A=1.2+2.3+3.4+…+n.(n+1)$
$⇒3A=3.[1.2+2.3+3.4+…+n.(n+1)]$
$⇒3A=1.2.3+2.3.3+3.4.3+…+n.(n+1).3$
$⇒3A=1.2.3+2.3.(4-1)+3.4.(5-2)+...+n.(n+1).[(n+2)-(n-1)]$
$⇒3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+n.(n+1).(n+2)-(n-1).n.(n+1)$
$⇒3A=n.(n+1).(n+2)$
$⇒A=\dfrac{n.(n+1).(n+2)}{3}$
$A = 1.2 + 2.3 + 3.4 + … + n.(n + 1)$
$⇔ 3A =1.2.3 + 2.3.3 + 3.4.3 + ... + n.(n+1).3$
$⇔ 3A = 1.2.3 + 2.3.(4-1) + 3.4.(5-2) + ..... + n.(n+1).[n+2-(n-1)]$
$⇔ 3A = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ..... + n.(n+1).(n+2) - (n-1).n.(n+1)$
$⇔ 3A = n.(n+1).(n+2)$
$⇔ A = \dfrac{n.(n+1).(n+2)}{3}$
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