Question

Tính:

S = 1 . 2 + 2 . 3 + 3 . 4 + 4 . 5 +......+ 99 . 100

Answer 1

S = 1 . 2 + 2 . 3 + 3 . 4 + 4 . 5 +......+ 99 . 100

3S=1.2.3+2.3.(4-1)+...+99.100.(101-98) 3S=1.2.3+2.3.4-1.2.3+...+99.100.101-98.99.100 3S=99.100.101=999900 S=999900/3=333300

Answer 2

S= 1.2+2.3+3.4+4.5+...+99.100

3.S=1.2.3+2.3.(4-1)+3.4.(5-2)+4.5.(6-3)+...+99.100.(101-98)

3S-S=1.2.3+2.3.(4-1)-1.2.3+3.4.(5-2)-2.3.(4-1)+4.5.(6-3)-3.4.(5-2)+...+99.100.(101-98)-98.99.(100-97)

S=(99.100.101):3=333300