`D=1/2.5+1/5.8+1/8.11+...+1/1979.1982`

`=3/3(1/2.5+1/5.8+1/8.11+...+1/1979.1982)`

`=1/3(3/2.5+3/5.8+3/8.11+...+3/1979.1982)`

`=1/3(1/2-1/5+1/5-1/8+1/8-1/11+...+1/1979-1/1982)`

`=1/3(1/2-1/1982)`

`=1/3(991/1982-1/1982)`

`=1/3 . 495/991`

`=165/991`

nay tui con thay

\(\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+...+\frac{1}{98.101}\)

\(=\frac{1}{3}.\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{98}-\frac{1}{101}\right)\)

\(=\frac{1}{3}.\left(\frac{1}{2}-\frac{1}{101}\right)\)

\(=\frac{1}{3}\cdot\frac{99}{202}=\frac{33}{202}\)

sửa lại đề 1 chút : 

\(\frac{1}{2\cdot5}+\frac{1}{5\cdot8}+\frac{1}{8\cdot11}+...+\frac{1}{98\cdot101}\)

\(=\frac{1}{3}\left(\frac{3}{2\cdot5}+\frac{3}{5\cdot8}+\frac{3}{8\cdot11}+...+\frac{3}{98\cdot101}\right)\)

\(=\frac{1}{3}\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{98}-\frac{1}{101}\right)\)

\(=\frac{1}{3}\left(\frac{1}{2}-\frac{1}{101}\right)\)

\(=\frac{1}{3}\cdot\frac{99}{202}\)

\(=\frac{33}{202}\)

tham khảo ở đây nha

https://olm.vn/hoi-dap/detail/222956295982.html

\(A=\dfrac{1}{3}\left(\dfrac{1}{2}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{11}+...+\dfrac{1}{150}-\dfrac{1}{153}\right)\)

\(=\dfrac{1}{3}.\dfrac{151}{306}=\dfrac{151}{918}\)

=21​−51​+51​−71​+....+951​−981​

=12−198=21​−981​tự làm tiếp

A = 1/2.5 + 1/5.8 + 1/8.11 + ... + 1/92.95 + 1/95.98

A = 1/3 . ( 3/2.5 + 3/5.8 + 3/8.11 + ... + 3/92.95 + 3/95.98 )

A = 1/3 . ( 1/2 - 1/5 + 1/5 - 1/8 + 1/8 - 1/11 + ... + 1/92 - 1/95 + 1/95 - 1/98 )

A = 1/3 . ( 1/2 - 1/98 )

A = 1/3 . 24/49

A = 8/49 tick cho tui

Đặt A=1/2.5+1/5.8+...+1/(3n-1)(3n+2)

3A=3/2.5+3/5.8+....+3/(3n-1)(3n+2)

3A=1/2-1/5+1/5-1/8+....+1/3n-1-1/3n+2

3A=1/2-1/3n+2

3A=3n/6n+4

A=(3n/6n+4) /3

A=n/6n+4(đpcm)

nhân 3 vào cả hai vế 

đáp án:307/1830

=1/3.3(1/2.5-1/5.8-1/8.11-...-1/302.305)

=1/3.(3/2.5-3/5.8-3/8.11-...-3/302.305)

=1/3(1/2-1/5-1/5-1/8-1/8-1/11-...-1/302-1/305)

=1/3[(1/2-1/305)+(1/5-1/5)+...+(1/302-1/302)

=1/3*(1/2-1/305)=1/3*(305/610-1/610)=1/3*304/610=152/915

hình như mình làm sai hoặc sai đề , sao số lớn ghê

1/2.5+1/5.8+1/8.11+...+1/29.32 (khoảng cách từ 2-5;5-8;8-11;...;29-32 là 3) suy ra

=1/3(1/2-1/5+1/5-1/8+1/8-1/11+...+1/29-1/32)  (-1/5+1/5;-1/8+1/8;-1/11+1/11=0) suy ra =1/3(1/2-1/32)=1/3.15/32=5/32

1/2.5+1/5.8+1/8.9+............+1/29.32

=1/2-1/5+1/5-1/8+...............+1/29-1/32

=1/2-1/32

=15/32

ai tích mk=>mk tích lại