$Đặt:S=1.2.3+2.3.4+3.4.5+…+98.99.100\\4S=4(1.2.3+2.3.4+3.4.5+…+98.99.100)\\S=1.2.3.4+2.3.4.4+3.4.5.4+…+98.99.100.4\\S=1.2.3.(4-0)+2.3.4.(5-1)+3.4.5.(6-2)+…+98.99.100.(101-97)\\\text{Ta đi phân tích các biểu thức như sau,Ta có:}\\1.2.3.(4-0)=1.2.3.4-0.1.2.3\\2.3.4.(5-1)=2.3.4.5-1.2.3.4\\3.4.5.(6-2)=3.4.5.6-2.3.4.5\\………………..\\98.99.100.(101-97)=98.99.100.101-97.98.99.100\\\text{Khi đó,S trở thành:}\\S=1.2.3.4-0.1.2.3+2.3.4.5-1.2.3.4+3.4.5.6-2.3.4.5+…+98.99.100.101-97.98.99.100\\S=\frac{98.99.100.101}{4}\\S=\frac{98.99.25.4.101}{4}\\S=\frac{98.99.25.\not4.101}{\not4}\\S=98.99.25.101\\S=24497550$
Đáp án + Giải thích các bước giải:
$P=1.2.3+2.3.4+3.4.5+…+98.99.100$
$4P= 4(1.2.3+2.3.4+3.4.5+…+98.99.100)$
$4P= 1.2.3.4+2.3.4.4+3.4.5.4+…+98.99.100.4$
$4P=1.2.3.4+2.3.4.(5-1)+3.4.5.(6-2)+…+98.99.100.(101-97)$
$4P=1.2.3.4+2.3.4.5-1.2.3.4+3.4.5.6-2.3.4.5+…+98.99.100.101-97.98.99.100$
$4P=98.99.100.101=97990200$
$→ P=\dfrac{97990200}4=24497550$
$Đặt:S=1.2.3+2.3.4+3.4.5+…+98.99.100\\4S=4(1.2.3+2.3.4+3.4.5+…+98.99.100)\\S=1.2.3.4+2.3.4.4+3.4.5.4+…+98.99.100.4\\S=1.2.3.(4-0)+2.3.4.(5-1)+3.4.5.(6-2)+…+98.99.100.(101-97)\\\text{Ta đi phân tích các biểu thức như sau,Ta có:}\\1.2.3.(4-0)=1.2.3.4-0.1.2.3\\2.3.4.(5-1)=2.3.4.5-1.2.3.4\\3.4.5.(6-2)=3.4.5.6-2.3.4.5\\………………..\\98.99.100.(101-97)=98.99.100.101-97.98.99.100\\\text{Khi đó,S trở thành:}\\S=1.2.3.4-0.1.2.3+2.3.4.5-1.2.3.4+3.4.5.6-2.3.4.5+…+98.99.100.101-97.98.99.100\\S=\frac{98.99.100.101}{4}\\S=\frac{98.99.25.4.101}{4}\\S=\frac{98.99.25.\not4.101}{\not4}\\S=98.99.25.101\\S=24497550$