Question

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

Answer 1

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

3A = 1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+.+99.100.101-98.99.100

3A = 99.100.101

Answer 2

Đặt A= 1.2+2.3 +.......+99.100

3A= 1.2.3+2.3.4+3.4.3 +......+ 99.100.3

3A= 1.2. (3 - 0) + 2.3.(4 - 1) +3.4. (5 - 2)....... . 99.100. (101 - 98)

3A = (1.2.3 + 2.3.4 + 3.4.5 +...... + 99.100.101) - (0.1.2 + 1.2.3 + 2.3.4 +.......+ 98.99.100)

3A = 99.100.101 - 0.1.2

3A = 999900 - 0

3A= 999900

A= 999900 : 3

A = 333300

Answer 3

S = 1.2 + 2.3 + 3.4 + . + 99.100

3S = 1.2.3+2.3.3+3.4.3+...+98.99.3+99.100.3

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

= 1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...-97.98.99+99.100.101-98.99.100

3S= 99.100.101

=> S = 33.100.101 = 333300

Answer 4

\(S=1.2+2.3+3.4+....+99.100\)

     \(=1.\left(1-2+2-3+3-4+....99-100\right)\)

     \(=1.\left(1-100\right)\)

     \(=1.\left(-99\right)\)

     \(=-99\)