Giải thích các bước giải:
$A=1.2+2.3+3.4+..+1999.2000$
$\rightarrow 3A=1.2.3+2.3.3+3.4.3+..+1999.2000.3$
$\rightarrow 3A=1.2.(3-0)+2.3.(4-1)+3.4.(5-2)+..+1999.2000.(2001-1998)$
$\rightarrow 3A=1.2.3-0.1.2+2.3.4-1.2.3+3.4.5-2.3.4+..+1999.2000.2001-1998.1999.2000$
$\rightarrow 3A=1999.2000.2001$
$\rightarrow A=\dfrac{1999.2000.2001}{3}$
$B=1.1+2.2+3.3+..+1999.1999$
$\rightarrow B=1.(2-1)+2.(3-1)+3.(4-1)+..+1999.(2000-1)$
$\rightarrow B=1.2+2.3+3.4+..+1999.2000-(1+2+3+..+1999)$
$\rightarrow B=\dfrac{1999.2000.2001}{3}-\dfrac{1999.(1+1999)}{2}$
$\rightarrow B=\dfrac{1999.2000.2001}{3}-\dfrac{1999.2000}{2}$
$C=1.2.3+2.3.4+..+48.49.50$
$\rightarrow 4C=1.2.3.4+2.3.4.4+..+48.49.50.4$
$\rightarrow 4C=1.2.3.(4-0)+2.3.4.(5-1)+..+48.49.50.(51-47)$
$\rightarrow 4C=1.2.3.4-0.1.2.3.4+2.3.4.5-1.2.3.4+..+48.49.50.51-47.48.49.50$
$\rightarrow 4C=48.49.50.51$
$\rightarrow C=\dfrac{48.49.50.51}{4}$
