C=4/2.4+4/4.6+4/6.8+...+4/2008.2010
 C = 2 ( 2 / 2.4 + 2/4.6 + 2/6.8 + ...+2/2008.2010)
 C = 2 ( 1 - 1/4 + 1/4 - 1/6+1/6 - 1/8 +....+1/2008 - 1/2010 )
 C = 2 ( 1 - 1 / 2010 )
 C = 2 . 2009/2010 
 C = 2009 / 1005
Chúc bạn học tốt !

bạn tách ra từng bài một mình sẽ giúp 

B = \(\frac{1}{25.27}\)+ \(\frac{1}{27.29}+\frac{1}{29.31}+...+\frac{1}{73.75}\)
2B = 2 ( 1/25.27+1/27.29+1/29.31+...+1/73.75)  Mình x 2 lên tí phải chia cho 2
2B = \(\frac{2}{25.27}+\frac{2}{27.29}+...+\frac{2}{73.75}\)
2B = 1/25 - 1/27+ 1/27-1/29 + .... + 1/73 - 1/75
2B = 1/25 - 1/75
2B = 3/75 - 1/75
2B = 2/75
=> B = 2/75 : 2
  B = 2/75 . 1/2
  B = 1/75
Chúc bạn học tốt 

\(a,\frac{1}{3}x+\frac{2}{5}x-\frac{2}{5}=0\)

\(\frac{11}{15}x=\frac{2}{5}\)

\(x=\frac{6}{11}\)

b,\(\left(2x-3\right).\left(6-2x\right)=0\)

\(\Rightarrow\orbr{\begin{cases}2x-3=0\\6-2x=0\end{cases}\Rightarrow}\orbr{\begin{cases}x=\frac{3}{2}\\x=3\end{cases}}\)

Vậy

\(\left(3x-1\right).\left(-\frac{1}{2}x+5\right)=0\)
\(\Rightarrow\orbr{\begin{cases}3x-1=0\\-\frac{1}{2}x+5=0\end{cases}\Rightarrow\orbr{\begin{cases}x=\frac{1}{3}\\x=10\end{cases}}}\)\

Vậy

\(S=\frac{1}{1.3}-\frac{1}{2.4}+\frac{1}{3.5}-\frac{1}{4.6}+\frac{1}{5.7}-\frac{1}{6.8}+\frac{1}{7.9}-\frac{1}{8.10}\)

\(S=\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{2}-\frac{1}{4}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{7}-\frac{1}{9}=\frac{1}{8}-\frac{1}{10}\right)\)

\(S=\frac{1}{2}\left(1+\frac{1}{2}-\frac{1}{9}-\frac{1}{10}\right)\)

\(S=\frac{1}{2}.\left(\frac{58}{45}\right)\)

\(S=\frac{29}{45}\)

S =1/1.3-1/2.4+1/3.5-1/4.6+1/5.7 - 1/6.8+1/7.9-1/8.10

\(=\left(\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{7.9}\right)+\left(\frac{1}{2.4}+\frac{1}{4.6}+...+\frac{1}{8.10}\right)\)

\(=\frac{1}{2}\left(\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{7.9}\right)+\frac{1}{2}\left(\frac{1}{2.4}+\frac{1}{4.6}+...+\frac{1}{8.10}\right)\)

\(=\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{7}-\frac{1}{9}\right)+\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{8}-\frac{1}{10}\right)\)

\(=\left(1-\frac{1}{9}\right)+\left(\frac{1}{2}-\frac{1}{10}\right)\)

\(=\frac{8}{9}+\frac{2}{5}\)

\(=\frac{58}{45}\)

viết đề hẳn hoi đi đề thì xấu còn bày đặt làm càn

\(S=\frac{1}{1.3}-\frac{1}{2.4}+\frac{1}{3.5}-\frac{1}{4.6}+\frac{1}{5.7}-\frac{1}{6.8}+\frac{1}{7.9}-\frac{1}{8.10}\)

\(S=\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}\right)-\frac{1}{2.4}-\frac{1}{4.6}-\frac{1}{6.8}-\frac{1}{8.10}\)

\(S=\frac{1}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}\right)-\left(\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+\frac{1}{8.10}\right)\)

\(S=\frac{1}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}\right)-\frac{1}{2}\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+\frac{2}{8.10}\right)\)

\(S=\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}\right)-\frac{1}{2}\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+\frac{1}{8}-\frac{1}{10}\right)\)

\(S=\frac{1}{2}\left(1-\frac{1}{9}\right)-\frac{1}{2}\left(\frac{1}{2}-\frac{1}{10}\right)\)

\(S=\frac{1}{2}\left(1-\frac{1}{9}-\frac{1}{2}+\frac{1}{10}\right)\)

\(S=\frac{1}{2}.\frac{22}{45}=\frac{11}{45}\)

\(S=\frac{1}{1.3}-\frac{1}{2.4}+\frac{1}{3.5}-\frac{1}{4.6}+\frac{1}{5.7}-\frac{1}{6.8}+\frac{1}{7.9}-\frac{1}{8.10}\)

\(S=\frac{1}{2}.\left[\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}\right)-\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+\frac{2}{8.10}\right)\right]\)

\(S=\frac{1}{2}.\left[\left(1-\frac{1}{3}+...+\frac{1}{7}-\frac{1}{9}\right)-\left(\frac{1}{2}-\frac{1}{4}+...+\frac{1}{8}-\frac{1}{10}\right)\right]\)

\(S=\frac{1}{2}.\left[\left(1-\frac{1}{9}\right)-\left(\frac{1}{2}-\frac{1}{10}\right)\right]\)

\(S=\frac{1}{2}.\left(\frac{8}{9}-\frac{2}{5}\right)\)

\(S=\frac{1}{2}.\frac{22}{45}=\frac{11}{45}\)

\(S=\frac{1}{1.3}-\frac{1}{2.4}+\frac{1}{3.5}-\frac{1}{4.6}+\frac{1}{5.7}-\frac{1}{6.8}+\frac{1}{7.9}-\frac{1}{8.10}\)

=> \(S=\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}\right)+\left(\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+\frac{1}{8.10}\right)\)

=> \(S=\frac{1}{2}\left(1-\frac{1}{3}+.....+\frac{1}{7}-\frac{1}{9}\right)+\frac{1}{2}\left(\frac{1}{2}-\frac{1}{4}+....+\frac{1}{8}-\frac{1}{10}\right)\)

=> \(S=\frac{1}{2}\left(1-\frac{1}{9}\right)+\frac{1}{2}\left(\frac{1}{2}-\frac{1}{10}\right)\)

=> \(S=\frac{1}{2}.\frac{8}{9}+\frac{1}{2}.\frac{2}{5}\)

=> \(S=\frac{4}{9}+\frac{1}{5}\)

=> \(S=\frac{29}{45}\)

1/1.3 - 1/2.4 + 1/3.5 - 1/4.6 + ...+ 1/97.99 - 1/98.100 + 3lxl = 1 

tách ra trc đầu tiên tính phần : 1/1.3 - 1/2.4 + 1/3.5 - 1/4.6 + ...+ 1/97.99 - 1/98.100

tách số lẻ và số chẵn ra 

(1/1.3+1/3.5+...+1/57.97+1/97.99)-(1/2.4+1/4.6+...1/98.100)

tính từng vế  vế đầu kết qu3 vế lẻ là : 49/99 

kết quả vế chẵn là 49/200

thì bài đó sẻ thành : 49/99+49/200+3lxl=1 

còn lại tự tinh nha