Question

1.2+2.3+3.4+4.5+....+99.100

 

Answer 1

Đặt A = 1.2 + 2.3 + 3.4 + 4.5 + ... + 99.100

3A = 1.2.(3-0) + 2.3.(4-1) + 3.4.(5-2) + 4.5.(6-3) + ... + 99.100.(101-98)

3A = 1.2.3 - 0.1.2 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + 4.5.6 - 3.4.5 + ... + 99.100.101 - 98.99.100

3A = 99.100.101

A = 33.100.101

A = 333300

Answer 2

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

3A=1.2.3+2.3.3+3.4.3+...+99.100.3=1.2(3-0)+2.3(4-1)+3.4(5-2)+...+99.100(101-98)=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+99.100.101-99.100.98=99.100.101

Vậy A= 99.101.100/3

Answer 3

dung xich ma  \sum_1^99 x(x+1) = 333300

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Answer 4

Đặt A = 1.2 + 2.3 + 3.4 + 4.5 + ... + 99.100

3A = 1.2.(3-0) + 2.3.(4-1) + 3.4.(5-2) + 4.5.(6-3) + ... + 99.100.(101-98)

3A = 1.2.3 - 0.1.2 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + 4.5.6 - 3.4.5 + ... + 99.100.101 - 98.99.100

3A = 99.100.101

A = 33.100.101

A = 333300