Question

tính A=1.4+2.5+3.6+...+99.102

Answer 1

A = 1.4 + 2.5 + 3.6 + ... + 99.102

A = 1.(2 + 2) + 2.(3 + 2) + 3.(4 + 2) + ... + 99.(100 + 2)

A = (1.2 + 2.3 + 3.4 + ... + 99.100) + (1.2 + 2.2 + 3.2 + ... + 99.2)

Đặt B = 1.2 + 2.3 + 3.4 + ... + 99.100

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

3B = 1.2.3 - 0.1.2 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ... + 99.100.101 - 98.99.100

3B = 99.100.101

B = 33.100.101 = 333300

A = 333300 + 2.(1 + 2 + 3 + ... + 99)

A = 333300 + 2.(1 + 99).99:2

A = 333300 + 100.99

A = 333300 + 9900

A = 343200