Question

Tính tổng 1 .2 + 2.3 + 3.4 +4.5+.............+49 . 50

Answer 1

A=1.2+2.3+...+49.50

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

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

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

=>3A=49.50.51

=>A=49.25.51=62475

=>3A=

Answer 2

Đặt A=1.2+2.3+3.4+4.5+...+49.50

3A=1.2.3+2.3.3+3.4.3+4.5.3+...+49.50.3

3A=1.2.(3-0)+2.3.(4-1)+3.4.(5-2)+4.5.(6-3)+...+49.50.(51-48)

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+...+49.50.51-48.49.50

3A=(1.2.3+2.3.4+3.4.5+4.5.6+...+49.50.51)-(0.1.2+1.2.3+2.3.4+3.4.5+...+48.49.50)

3A=49.50.51-0.1.2

3A=49.50.51

A=49.50.17

A=41650

Answer 3

đặt S làm tên biểu thức trên

ta có :

S =  1 .2 + 2.3 + 3.4 +4.5+.............+49 . 50

3S = 1.2.3 + 2.3.3 + 3.4.3 + 4.5.4 + ... + 49.50.3

3S = 1.2.3 + 2.3.(4-1) + 3.4.(5-2) + 4.5.(6-3 ) + ... + 49.50.(51 - 48 )

3S = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + 4.5.6 - 3.4.5 + ... + 49.50.51 - 48.49.50

3S = 49.50.51

S = 49.50.51 : 3

S = 41650