Question

Tính tổng:

A = 1*2+2*3+3*4+...............+49*50

 

Answer 1

A=1.2+2.3+3.4+...+49.50

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

3A=1.2.(3-0)+2.3.(4-1)+3.4.(5-2)+...+49.50.(51-48)

3A=1.2.3-0.1.2+2.3.4+1.2.3+3.4.5-2.3.4+...+49.50.51-48.49.50

3A=(1.2.3+2.3.4+3.4.5+...+49.50.51) - (0.1.2+1.2.3+2.3.4+...+48.49.50)

3A=49.50.51-0.1.2

3A=49.50.51-0

3A=49.50.51

A=49.50.17

A=41650

Answer 2

A = 1*2+2*3+3*4+...............+49*50

A=41650

Answer 3

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

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

A.3 = 49.50.51

A.3 = 124950

  A = 124950 : 3

  A = 41650

Answer 4

    A=1x2+2x3+3x4+....+49x50

Ax3=1x2x3+2x3x3+3x4x3+......+49x50x3

Ax3=1x2x3 + 2x3x(4-1) + 3x4x(5-2)+.....+49x50x(51-47)

Ax3=1x2x3 + 2x3x4 - 1x2x3 +3x4x5 - 2x3x4 + 4x5x6 -3x4x5 + ...... + 49x50x51 - 48x49x50

Ax3= 49 x50 x51

A= 49 x 50 x 51 : 3

A=41650