Question

tính S = 1.3+2.4+3.5+.....+48.50+49.51

Answer 1

S = 1.3+2.4+3.5+ .....+48.50+49.51 

S = 1(2 + 1) + 2(3 + 1) + 3(4 + 1) + ... + 48(49 + 1) + 49(50 + 1)

S =1 + 1.2 + 2.3 + 2 + 3.4 + 3 + ... + 48.49 + 48 + 49.50 + 49

S = (1 + 2 + 3 + ... + 49) + (1.2 + 2.3 + 3.4 + ... + 49.50)

đặt A  = 1 + 2 + 3 + ... + 49

A = (49 + 1).49 : 2

A = 1225

đătj B = 1.2 + 2.3 + 3.4 + ... + 49.50

3B = 1.2.3 + 2.3.3 + 3.4.3 + ... + 49.50.3

3B = 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) + ... + 49.50.(51 - 48)

3B = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ... + 49.50.51 - 48.49.50

3B = 49.50.51

B = 41650

=> S = A + B = 41650 + 1225 = 42875

Answer 2

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