Question

Tính A

A = 1 . 2 . 3 + 2 . 3 . 4 + 3 . 4 . 5 + .....+ 98 . 99 . 100

Answer 1

A=1.2.3+2.3.4+3.4.5+...+98.99.100

4A=1.2.3.4+2.3.4.4+3.4.5.4+...+98.99.100.4

4A=1.2.3.(4-0)+2.3.4.(5-1)+...+98.99.100.(101-97)

4A=1.2.3.4+2.3.4.5-1.2.3.4+...+98.99.100.101-97.98.99.100

4A=1.2.3.4-1.2.3.4+2.3.4.5-...-97.98.99.100+98.99.100.101

4A=98.99.100.101

4A=97990200

A=\(\frac{\text{97990200}}{4}\)

A=24497550

Answer 2

A = 1.2.3+2.3.4+3.4.5+...+98.99.100

4.A= 1.2.3.4+2.3.4.(5-1)+3.4.5.(6-2)+...+98.99.100.(101-97)

4A-A= 1.2.3.4+2.3.4.(5-1)-1.2.3.4+3.4.5.(6-2)-2.3.4.(5-1)+...+98.99.100.(101-97)-97.98.99.(100-96)

A = 98.99.100.101:4=24497550