Gọi biểu thức cần tình giá trị là A.

Ta có: \(A=\dfrac{1}{4.8}+\dfrac{1}{8.12}+\dfrac{1}{12.16}+...+\dfrac{1}{2008.2012}\)

\(\Leftrightarrow4A=4\left(\dfrac{1}{4.8}+\dfrac{1}{8.12}+\dfrac{1}{12.16}+...+\dfrac{1}{2008.2012}\right)\)

\(\Leftrightarrow4A=\dfrac{1}{4}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{12}+\dfrac{1}{12}-\dfrac{1}{16}+...+\dfrac{1}{2008}-\dfrac{1}{2012}\)

\(\Leftrightarrow4A=\dfrac{1}{4}-\dfrac{1}{2012}=\dfrac{251}{1006}\)

\(\Leftrightarrow A=\dfrac{\dfrac{251}{1006}}{4}=\dfrac{251}{4024}\)

Ta gọi Biểu thức trên là A ta có:

A= \(\dfrac{1}{4.8}+\dfrac{1}{8.12}+\dfrac{1}{12.16}+...+\dfrac{1}{2008.2012}\)

4.A=\(\dfrac{4}{4.8}+\dfrac{4}{8.12}+\dfrac{4}{12.16}+...+\dfrac{4}{2008.201}\)

4.A=\(\dfrac{1}{4}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{12}+\dfrac{1}{12}-\dfrac{1}{16}+...+\dfrac{1}{2008}-\dfrac{1}{2012}\)

4.A=\(\dfrac{1}{4}-\dfrac{1}{2012}\)

4.A=\(\dfrac{502}{2012}\)

  A=\(\dfrac{502}{2012}:4\)

  A=\(\dfrac{502}{8048}\)

  A=\(\dfrac{251}{4024}\)

  Vậy biểu thức trên có giá trị là \(\dfrac{251}{4024}\)

\(\dfrac{1.2+2.4+3.6+4.8+5.10}{3.4+6.8+9.12+12.16+15.20}\)

\(=\dfrac{1.2+2.4+3.6+4.8+5.10}{3.4+3.4.2.2+3.4.3.3+3.4.2.8+3.4.5.5}\)

\(=\dfrac{1.2.\left(4+3^2+2.8+5^2\right)}{3.4.\left(4+3^2+2.8+5^2\right)}\)

\(=\dfrac{1}{6}\)

\(\dfrac{1.2+2.4+3.6+4.8+5.10}{3.4+6.8+9.12+12.16+15.20}\)

\(=\dfrac{1.2+1.2.2^2+1.2.3^2+1.2.4^2+1.2.5^2}{3.4+3.4.2^2+3.4.3^2+3.4.4^2+3.4.5^2}\)

\(=\dfrac{1.2\left(1+2^2+3^2+4^2+5^2\right)}{3.4\left(1+2^2+3^2+4^2+5^2\right)}\\ =\dfrac{2}{12}=\dfrac{1}{6}\)

\(\dfrac{1.2+2.4+3.6+4.8+5.10}{3.4+6.8+9.12+12.16+15.20}\)

= \(\dfrac{2\left(1+4+9+16+25\right)}{4\left(3+12+27+48+65\right)}\)

= \(\dfrac{2.55}{4.155}\)

= \(\dfrac{1.55}{2.155}\)

= \(\dfrac{55}{310}=\dfrac{11}{62}\)

1/6 uyhvnb

Ý ban là:

\(\frac{1}{6}\)

Lục Minh Hoàng cho mình hỏi tại sao lại có 1/2 vậy ?

1/3+1/15+1/35+1/63+1/99+1/143+1/195

=1/1*3+1/3*5+1/5*7+1/7*9+1/9*11+1/11*13+1/13*15

suy ra 2(1/1*3+1/3*5+1/5*7+1/7*9+1/9*11+1/11*13+1/13*15)

=2/1*3+2/3*5+2/5*7+2/7*9+2/9*11+2/11*13+2/13*15

=1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13+1/13-1/15

=1-1/15

=14/15

a=14/15 chia 2=7/15

a: \(=\left(\dfrac{28}{42}+\dfrac{12}{42}-\dfrac{3}{42}\right):\left(\dfrac{-28}{28}-\dfrac{12}{28}+\dfrac{3}{28}\right)\)

\(=\dfrac{37}{42}:\dfrac{-37}{28}=\dfrac{-28}{42}=-\dfrac{2}{3}\)

b: \(=\dfrac{2+8+18+32+50}{12+48+108+192+300}=\dfrac{110}{660}=\dfrac{1}{6}\)

= \(\frac{1.2+2.4+3.6+4.8+5.10}{3.2\left(1.2+2.4+3.6+4.8+5.10\right)}=\frac{1}{6}\)
nha :*