Question

Tính  \(B=1.2+2.3+3.4+......+100.101\)

Answer 1

B=1.2+2.3+3.4+...+100.101

=>3B=1.2.3+2.3.3+3.4.4+....+100.101.3

=1.2.3-0.1.2+2.3.4-1.2.3+3.4.5-2.3.4+....+100.101.102-99.100.101

=-0.1.2-100.101.102

=1030200

=>B=1030200:3=343400

Answer 2

B = 1.2+2.3 +.......+99.100+100.101

3B= 1.2.3+2.3.4+3.4.3 +......+ 99.100.3 + 100.101.3

3B= 1.2. (3 - 0) + 2.3.(4 - 1) +3.4. (5 - 2)....... . 99.100. (101 - 98) . 100.101.(102 - 99)

3B = (1.2.3 + 2.3.4 + 3.4.5 +...... + 99.100.101 + 100.101.102) - (0.1.2 + 1.2.3 + 2.3.4 +.......+ 98.99.100.99.100.101)

3B = 100.101.102 - 0.1.2

3B = 1030200 - 0

3B= 1030200

B =  1030200 : 3

B =  343400

Answer 3

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