Ta có : S = 1.2 + 2.3 + 3.4 + ..... + 32.33

=> 3S = 1.2.3 - 1.2.3 + 2.3.4 - 2.3.4 + ...... + 32.33.34

=> 3S = 32.33.34

=> S = \(\frac{32.33.34}{3}=11968\)

3S=1*2*3+2*3*(4-1)+...+99*100*(101-98)

=1*2*3+2*3*4-1*2*3+...+99*100*101-99*100*98

=99*100*101

=>S=33*100*101=333300

Số các số hạng của A là :

( 99 - 1 ) : 1 + 1 = 99 ( số )

Tổng A là :

( 99 + 1 ) . 99 : 2 = 4950

Vậy tổng A = 4950 .

Bạn nhân 3 lên

Mk ko ghi lại đề bài mà làm tiếp luôn nhé!

3A=1.2.3+2.3.3+3.4.3+.......+98.99.3

3A=1.2.3+2.3.(4-1)+3.4.(5-2)+.........+98.99.(100-97)

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

3A=98.99.100

A=98.99.100/3

Bn k cho mk nhé!

B= 

A = 1.2+2.3+3.4+.........................+1999.2000 

=> 3A= 1.2.(3-0) + 2.3.(4-1) + ... + 1999.2000(2001-1998)

=> 3A=1.2.3+2.3.4-1.2.3+...+1999.2000.2001-1998.1999.2000

=> 3A=1999.2000.2001

A=1999.2000.2001:3=2666666000

=> 3A = 1.2.3 + 2.3.3 + 3.4.3 + ...+ 123.124.3

3A = 1.2.(3 - 0) + 2.3.(4 - 1) + 3.4.(5 - 2) + ... + 123.124.(125 - 122)

3A = 1.2.3 - 1.2.0 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ...+ 123.124.125 - 122.123.124

3A = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ...+ 123.124.125 - 122.123.124

3A = 123.124.125

=> A = \(\frac{123.124.125}{3}=635500\)

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

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

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

3A = 48.49.50 = 117600

A = 39200 

Ta có :
Gọi A=1.2+2.3+3.4+4.5+...+49.50
 A=1.2+2.3+3.4+4.5+...+49.50
 3.A=3.(1.2+2.3+3.4+4.5+...+49.50)
 3.A=1.2.3+2.3.3+3.3.4+3.4.5+...+3.49.50
 3.A=1.2.(3-0)+2.3.(3-0)+(3-0).3.4+(3-0).4.5+...+(3-0).49.50
 3.A=1.2.3-0+2.3.3-0+3.3.4-0+3.4.5-0+...+3.49.50-0
 3.A=1.2.3-0+2.3.4-1.2.3+5.3.4-2.3.4+...+49.50.51-48.49.50
 3.A=49.50.51
 A= 49.50.51/3
 A= 49.50.17.3/3
 A=49.50.17
 A=41650
Đáp số : A=41650

1x2+2x3+3x4+4x5+...+49x50=A
3.(1.2+2.3+3.4+4.5+...+49.50)=A.3
3.1.2+3.2.3+3.3.4+3.4.5+...+3.49.50+A.3
(3-0).1.2+(4-1).2.3+(5-2).3.4+(6-3).4.5+...+(51-48).49.50=A.3
3.1.2-0.1.2+4.2.3-1.2.3+5.3.4-2.3.4+6.4.5-3.4.5+...+51.49.50-48,49,50=A.3
51.49.50=A.3
51.49.50:3=A
các bạn cứ tính kết quả ra là ok

\(A=1.2+2.3+3.4+...+2018.2019\)

\(3A=1.2.3+2.3.3+3.4.3+...+2018.2019.3\)

\(3A=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+2018.2019.\left(2020-2017\right)\)

\(3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+2018.2019.2020-2017.2018.2019\)

\(3A=2018.2019.2020\)

\(A=2018.673.2020\)

\(A=2743390280\)

Chúc bạn học tốt ~ 

Đặt A = 1x2 + 2x3 + 3x4 + ... + 99 x 100

3A = 1x2x3 + 2x3x3 + ... + 99x100x3

3A = 1x2x( 3 - 0 ) + 2x3x(4 - 1 ) +...+ 99x100x(101 - 98)

3A = ( 1x2x3 + 2x3x4 + ... + 99x100x101 ) - ( 0x1x2 + 1x2x3 +...+ 98x99x100)

3A = 99x100x101 - 0x1x2

3A = 99x100x101 - 0

A = 99x100x101 : 3

A = 333300

Vậy A = 3333000