Question

Tính A = 1.2 + 2.3 + 3.4 + .... + 99.100

Answer 1

A = 1.2 + 2.3 + 3.4 + .. + 99.100

<=> 3A = 1.2.3 + 2.3.3 + 3.4.3 +...+ 99.100.3

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

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

            = 999900

<=> A = 999900 : 3 = 333300

Answer 2

A=1.2+2.3+3.4+...+99.100

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+...+98.99.100+99.100.101 - 0.1.2-1.2.3-2.3.4-3.4.5-...-98.99.100

3A=99.100.101-0.1.2

3A=999900-0

3A=999900

A=999900:3

A=333300

Answer 3

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