\(B=2\left(\frac{5}{7.12}+\frac{5}{12.17}+...+\frac{5}{502.507}\right)\)

\(B=2\left(\frac{1}{7}-\frac{1}{12}+\frac{1}{12}-\frac{1}{17}+...+\frac{1}{502}-\frac{1}{507}\right)\)

\(B=2\left(\frac{1}{7}-\frac{1}{507}\right)\)

\(B=2\times\frac{500}{3549}\)

\(B=\frac{1000}{3549}\)

\(B=\frac{10}{7.12}+\frac{10}{12.17}+\frac{10}{17.22}+......+\frac{10}{502.507}\)

\(B=\frac{10}{5}.\left(\frac{5}{7.12}+\frac{5}{12.17}+\frac{5}{17.22}+........+\frac{5}{502.507}\right)\)

\(B=\frac{10}{5}.\left(\frac{1}{7}-\frac{1}{12}+\frac{1}{12}-\frac{1}{17}+\frac{1}{17}-\frac{1}{22}+.....+\frac{1}{502}-\frac{1}{507}\right)\)

\(B=\frac{10}{5}.\left(\frac{1}{7}-\frac{1}{507}\right)=2.\frac{500}{3549}=\frac{1000}{3549}\)

Nếu ai có giải dùm mình thì giải từng phần nhưng đừng chỉ ghi kết quả nhé~

a,\(\frac{2004}{10045}\)

b,\(\frac{25}{609}\)

c,\(\frac{1000}{3549}\)

d,\(\frac{25}{258}\)

A) \(\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+.....+\frac{1}{2006}-\frac{1}{2009}=\frac{1}{5}-\frac{1}{2009}=\frac{2004}{10045}\)các câu sau không theo quy luật bạn phải quy đồng mình đã giải xong câu a) rồi đấy bạn hãy vận dụng nó để giải các câu còn lại nên nhớ câu a) theo quy luật còn các câu còn lại không theo quy luật nên ta quy đồng không phải là mình không biết làm đâu => tại mình mỏi tay quá 

\(K=\frac{10}{7.12}+\frac{10}{12.17}+\frac{10}{17.22}+...+\frac{10}{502.507}\)

\(\Leftrightarrow K=\frac{10}{5}\left(\frac{1}{7}-\frac{1}{12}+\frac{1}{12}-\frac{1}{17}+\frac{1}{17}-\frac{1}{22}+...+\frac{1}{502}-\frac{1}{507}\right)\)

\(\Leftrightarrow K=2\left(\frac{1}{7}-\frac{1}{507}\right)\)

\(\Leftrightarrow K=2\cdot\frac{500}{3549}\)

\(\Leftrightarrow K=\frac{1000}{3549}\)

5xK=5/7.12+5/12.17+..............+5/502.507

5xK=(1/7-1/12)+(1/12-1/17)+........+(1/502-1/507)

5xK=1/7-1/507

5xK=500/3549

K   =500/3549:5

K    =100/3549

\(B=\frac{10}{7.12}+\frac{10}{12.17}+\frac{10}{17.22}+...+\frac{10}{2017.2022}\)

\(=2\left(\frac{5}{7.12}+\frac{5}{12.17}+\frac{5}{17.22}+...+\frac{5}{2017.2022}\right)\)

\(=2\left(\frac{1}{7}-\frac{1}{12}+\frac{1}{12}-\frac{1}{17}+...+\frac{1}{2017}-\frac{1}{2022}\right)\)

\(=2\left(\frac{1}{7}-\frac{1}{2022}\right)=\frac{2015}{7077}\)

\(B=\frac{10}{7.12}+\frac{10}{12.17}+\frac{10}{17.22}+...+\frac{10}{2017.2022}\)

\(\Rightarrow B=2.\left(\frac{5}{7.12}+\frac{5}{12.17}+\frac{5}{17.22}+...+\frac{5}{2017.2022}\right)\)

\(\Rightarrow B=2.\left(\frac{1}{7}-\frac{1}{12}+\frac{1}{12}-\frac{1}{17}+\frac{1}{17}-\frac{1}{22}+...+\frac{1}{2017}-\frac{1}{2022}\right)\)

\(\Rightarrow B=2.\left(\frac{1}{7}-\frac{1}{2022}\right)\)

\(\Rightarrow B=2.\frac{2015}{14154}\)

\(\Rightarrow B=\frac{2015}{7077}.\)

Vậy \(B=\frac{2015}{7077}.\)

Chúc bạn học tốt!

\(D=\dfrac{4}{8\cdot13}+\dfrac{4}{13\cdot18}+\dfrac{4}{18\cdot23}+...+\dfrac{4}{253\cdot258}\\ =\dfrac{4}{5}\cdot\dfrac{5}{8\cdot13}+\dfrac{4}{5}\cdot\dfrac{5}{13\cdot18}+\dfrac{4}{5}\cdot\dfrac{5}{18\cdot23}+...+\dfrac{4}{5}\cdot\dfrac{5}{253\cdot258}\\ =\dfrac{4}{5}\left(\dfrac{5}{8\cdot13}+\dfrac{5}{13\cdot18}+\dfrac{5}{18\cdot23}+...+\dfrac{5}{253\cdot258}\right)\\ =\dfrac{4}{5}\cdot\left(\dfrac{1}{8}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{18}+\dfrac{1}{18}-\dfrac{1}{23}+...+\dfrac{1}{253}-\dfrac{1}{258}\right)\\ =\dfrac{4}{5}\cdot\left(\dfrac{1}{8}-\dfrac{1}{258}\right)\\ =\dfrac{4}{5}\cdot\dfrac{125}{1032}\\ =\dfrac{25}{258}\)

ta có

Tính:

\(\dfrac{4}{8.13}+\dfrac{4}{13.18}+....+\dfrac{4}{253.258}\)

= 4 (\(\dfrac{1}{8.13}+\dfrac{1}{13.18}+.....+\dfrac{1}{253.258}\))

=\(\dfrac{4}{5}\left(\dfrac{1}{8}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{18}+...+\dfrac{1}{253}-\dfrac{1}{258}\right)\)

=\(\dfrac{4}{5}\left(\dfrac{1}{8}-\dfrac{1}{258}\right)\)

=\(\dfrac{25}{258}\)

\(N=2015+\frac{10}{2.7}+\frac{10}{7.12}+\frac{10}{12.17}+\frac{10}{17.22}\)

     \(=2\left(1007,5+\frac{5}{2.7}+\frac{5}{7.12}+\frac{5}{12.17}+\frac{5}{17.22}\right)\)

     \(=2\left(1007,5+\frac{7-2}{2.7}+\frac{12-7}{7.12}+\frac{17-12}{12.17}+\frac{22-17}{17.22}\right)\)

     \(=2\left(1007,5+\frac{1}{2}-\frac{1}{7}+\frac{1}{7}-\frac{1}{12}+\frac{1}{12}-\frac{1}{17}+\frac{1}{17}-\frac{1}{22}\right)\)

     \(=2\left(1007,5+\frac{1}{2}-\frac{1}{22}\right)\)

     \(=2015+1-\frac{1}{11}\)

     \(=\frac{22175}{11}\)

N = \(2015+\frac{10}{2,7}+\frac{10}{7,12}+\frac{10}{12,17}+\frac{10}{17,22}=2021.510611\)

\(N=2015+\frac{10}{2\cdot7}+\frac{10}{7\cdot12}+\frac{10}{12\cdot17}+\frac{10}{17\cdot22}=2015+2\left(\frac{5}{2\cdot7}+\frac{5}{7\cdot12}+\frac{5}{12\cdot17}+\frac{5}{17\cdot22}\right)\)\(=2015+2\left(\frac{1}{2}-\frac{1}{7}+\frac{1}{7}-\frac{1}{12}+\frac{1}{12}-\frac{1}{17}+\frac{1}{17}-\frac{1}{22}\right)\)

\(=2015+2\left[\left(\frac{1}{2}-\frac{1}{22}\right)+\left(\frac{1}{7}-\frac{1}{7}\right)+...+\left(\frac{1}{17}-\frac{1}{17}\right)\right]\)

\(=2015+2\left[\left(\frac{11}{22}-\frac{1}{22}\right)+0+...+0\right]=2015+2\cdot\frac{10}{22}=2015+\frac{10}{11}\)

xong rồi đó, cái còn lại thì bạn quy đồng rồi cộng nha

mk cũng ko chắc do tính nhẩm

\(\Rightarrow C=\frac{10}{5}\left(\frac{1}{7.12}+\frac{1}{12.17}+\frac{1}{17.22}+...+\frac{1}{502.507}\right)\)

\(\Rightarrow C=2.\left(\frac{1}{7}-\frac{1}{12}+\frac{1}{12}-\frac{1}{17}+....+\frac{1}{507}-\frac{1}{507}\right)\)

\(\Rightarrow C=2.\left(\frac{1}{7}-\frac{1}{507}\right)=2.\frac{1}{7}-2.\frac{1}{507}=\frac{2}{7}-\frac{2}{507}\)

\(B=\frac{10}{3\cdot8}+\frac{10}{8\cdot13}+\frac{10}{13\cdot18}+\frac{10}{18\cdot23}+\frac{10}{23\cdot28}\)

\(B=2\left[\frac{5}{3\cdot8}+\frac{5}{8\cdot13}+\frac{5}{13\cdot18}+\frac{5}{18\cdot23}+\frac{5}{23\cdot28}\right]\)

\(B=2\left[\frac{1}{3}-\frac{1}{8}+\frac{1}{8}-\frac{1}{13}+...+\frac{1}{23}-\frac{1}{28}\right]\)

\(B=2\left[\frac{1}{3}-\frac{1}{28}\right]=\frac{25}{42}\)

B = 10/3.8 + 10/8.13 + 10/13.18 + 10/18.23 + 10/23.28

   = 2.( 5/3.8 + 5/8.13 + 5/13.18 + 5/18.23 + 10/23.28 )

   = 2.( 1/3 -1/8 + 1/8 - 1/13 + 1/13 - 1/18 + 1/18 - 1/23 + 1/23 - 1/28 )

   = 2.( 1/3 - 1/28 )

   = 2. 25/84

   = 25/42

\(\frac{24}{42}\) nha bn  chúc hc tốtttt