S=1.2.3+2.3.4+3.4.5+...+88.89.90
⇒4S=4(1.2.3+2.3.4+3.4.5+...+88.89.90)
⇒4S= 1.2.3.4+2.3.4.4+3.4.5.4+...+88.89.90.4
⇒4S= 1.2.3.(4-0)+2.3.4.(5-1)+3.4.5.(6-2)+...+88.89.90.(91-87)
⇒4S= 1.2.3.4+2.3.4.5-1.2.3.4+3.4.5.6-2.3.4.5+...+88.89.90.91-87.88.89.90
⇒4S= 88.89.90.91
⇒4S=64144080
⇒S=$\frac{64144080}{4}$
⇒S=16036020
Vậy S=1.2.3+2.3.4+3.4.5+...+88.89.90=16036020
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