a=1.2+2.3+3.4+4.+....+200.201

3A = 1.2.(3 - 0) + 2.3.(4 - 1) + .... + 200.201.(202 - 199)

3A = 1.2.3 - 0.1.2 + 2.3.4 - 1.2.3 + .... + 200.201.202

3A = 200.201 . 202

A = 2706800

\(A=1.2+2.3+3.4+...+200.201\)

\(\frac{1}{A}=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{200.201}\)

\(\frac{1}{A}=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{200}-\frac{1}{201}\)

\(\frac{1}{A}=\frac{1}{1}-\frac{1}{201}=\frac{200}{201}\)

\(A=1:\frac{200}{201}=\frac{1.201}{200}=\frac{201}{200}\)

( Số cuối + Số đầu ) . số số hạng : 2 =a

\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+....+\frac{1}{200.201}\)

=\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{200}-\frac{1}{201}\)

=\(\frac{1}{2}-\frac{1}{201}\)

=\(\frac{199}{402}\)

\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{200.201}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{200}-\frac{1}{201}\)

\(=\frac{1}{2}-\frac{1}{201}=\frac{199}{402}\)

C=1*2+2*3+3*4+...+98*99

C=2+6+12+...+9702

C=2+9702

C=9704

vay C=9704

D=(1*99+2*99+3*99+...+99*99)-(1*2+2*3+3*4+...+98*99)

D=(99+198+297+...+9801)-(2+6+12+...+9702)

D=(99+9801)-(2+9702)

D=9900-9704

D=196

vay D=196

ai di qua dong tinh thi nho h cho minh nhe

D=1.2+2.3+3.4+...+2017.2018

=>3D=1.2.3+2.3.3+3.4.3+...+2017.2018.3

=>3D=1.2.(3-0)+2.3.(4-1)+3.4.(5-2)+...+2017.2018.(2019-2016)

=>3D=1.2.3-0.1.2+2.3.4-1.2.3+3.4.5-2.3.4+...+2017.2018.2019-2016.2017.2018

=>3D=\(\frac{2017.2018.2019}{3}\)

=>D=2739315938

Sửa lại dòng 2 từ cuối lên nhé là:

D=\(\frac{2017.2018.2019}{3}\)

cau hỏi tương tự ko có mà!!!!!!!!!!!!!!!!!!!!!!!!!!!!

3C=1.2.3+2.3.(4-1)+3.4.(5-2)+...+2014.2015.(2016-2013)

3C=2014.2015.2016

C=2014.2015.2016:3

D=1.2+2.3+3.4+...+99.100

=>3D=1.2.3+2.3.3+3.4.3+...+99.100.3

=1.2.3+2.3(4-1)+3.4(5-2)+...+99.100(101-98)

=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+....+99.100.101-98.99.100

=99.100.101=999900

=>D=333300

Đặt S= 1.2 + 2.3 + 3.4 + ...+ 99.100
 3S = 1.2.3+2.3.3+3.4.3+...+98.99.3+99.100.3
3S= 1.2.3+2.3(4-1)+3.4(5-2)+...+98.99(100-97)+99.100(101-98)
3S= 1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...-97.98.99+99.100.101-98.99.100
3S = 99.100.101  3S = 3.33.100.101 
 S=33.100.101= 333300

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

⇒ 3A = 1.2.3 + 2.3.3 + 3.4.3 + .... + 99.100.3

⇒ 3A = 1.2.3 + 2.3.( 4 - 1 ) + 3.4.( 5 - 2 ) + ..... + 99.100.( 101 - 98 )

⇒ 3A = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ..... + 99.100.101 - 98.99.100

⇒ 3A = ( 1.2.3 - 1.2.3 ) + ( 2.3.4 - 2.3.4 ) + .... + ( 98.99.100 - 98.99.100 ) + 99.100.101

⇒ 3A = 99.100.101

⇒ A = ( 99.100.101 ) : 3 = 333300

D= 1.2 + 2.3 + 3.4 + ............. + 90.91

3D = 1.2.3 + 2.3.3 + 3.4.3 + .... + 90.91.3

3D = 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) + ... + 90.91.(92 - 89)

3D = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ... + 90.91.92 - 89.90.91

3D = 90.91.92

D = 90.91.92 : 3 = 251160

Trả lời :

Bạn kia làm đúng rồi  ,bạn tham khảo nha !

Học tốt !