\(\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+.....+\frac{1}{946}+\frac{1}{99...">
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15 tháng 5 2016

\(M=\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+...+\frac{1}{946}+\frac{1}{990}\)

\(\Rightarrow\frac{1}{2}M=\frac{1}{2}\left(\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+...+\frac{1}{946}+\frac{1}{990}\right)\)

\(\Rightarrow\frac{1}{2}M=\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+...+\frac{1}{1892}+\frac{1}{1980}\)

\(\Rightarrow\frac{1}{2}M=\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+...+\frac{1}{43.44}+\frac{1}{44.45}\)

\(\Rightarrow\frac{1}{2}M=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{43}-\frac{1}{44}+\frac{1}{44}-\frac{1}{45}\)

\(\Rightarrow\frac{1}{2}M=\frac{1}{5}-\frac{1}{45}=\frac{9}{45}-\frac{1}{45}=\frac{8}{45}\)

\(\Rightarrow M=\frac{8}{45}:\frac{1}{2}=\frac{8}{45}.2=\frac{16}{45}\)

nhớ ấn đúng cho mình nha

15 tháng 5 2016

\(M=\frac{2}{30}+\frac{2}{42}+...+\frac{2}{1980}\)

\(=2\left(\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{44.45}\right)\)

\(=2\left(\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{44}-\frac{1}{45}\right)\)

\(=2\left(\frac{1}{5}-\frac{1}{45}\right)\)

\(=2\times\frac{8}{45}\)

\(=\frac{16}{45}\)

15 tháng 5 2016

Chào bạn, bạn hãy theo dõi bài giải của mình nhé!

\(\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+...+\frac{1}{946}+\frac{1}{990}\)

\(=\frac{2}{30}+\frac{2}{42}+\frac{2}{56}+...+\frac{2}{1892}+\frac{2}{1980}\)

\(=\frac{2}{5\cdot6}+\frac{2}{6\cdot7}+\frac{2}{7\cdot8}+...+\frac{2}{43\cdot44}+\frac{2}{44\cdot45}\)

\(=2\left(\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+...+\frac{1}{43\cdot44}+\frac{1}{44\cdot45}\right)\)

\(=2\left(\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{43}-\frac{1}{44}+\frac{1}{44}-\frac{1}{45}\right)\)

\(=2\left(\frac{1}{5}-\frac{1}{45}\right)=2\left(\frac{9}{45}-\frac{1}{45}\right)=2\cdot\frac{8}{45}=\frac{16}{45}\)

Chúc bạn học tốt!

19 tháng 5 2016

\(M=\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+...+\frac{1}{946}+\frac{1}{990}\)

\(M=\frac{2}{30}+\frac{2}{42}+...+\frac{2}{1980}\)

\(M=2\left(\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{44.45}\right)\)

\(M=2\left(\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{44}-\frac{1}{45}\right)\)

\(M=2\left(\frac{1}{5}-\frac{1}{45}\right)\)

\(M=2\times\frac{8}{45}\)

\(M=\frac{16}{45}\)

19 tháng 5 2016

\(M=\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+...+\frac{1}{946}+\frac{1}{990}\)

\(M=\frac{1\times2}{15\times2}+\frac{1\times2}{21\times2}+\frac{1\times2}{28\times2}+\frac{1\times2}{946\times2}+\frac{1\times2}{990\times2}\)

\(M=\frac{2}{30}+\frac{2}{42}+\frac{2}{56}+...+\frac{2}{1892}+\frac{2}{1980}\)

\(M=2\times\left(\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+...+\frac{1}{1892}+\frac{1}{1980}\right)\)

\(M=2\times\left(\frac{1}{5\times6}+\frac{1}{6\times7}+\frac{1}{7\times8}+...+\frac{1}{43\times44}+\frac{1}{44\times45}\right)\)

\(M=2\times\left(\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{43}-\frac{1}{44}+\frac{1}{44}-\frac{1}{45}\right)\)

\(M=2\times\left(\frac{1}{5}-\frac{1}{45}\right)\)

\(M=2\times\left(\frac{9}{45}-\frac{1}{45}\right)\)

\(M=2\times\frac{8}{45}\)

\(M=\frac{16}{45}\)

Chúc bạn học tốtok

18 tháng 5 2016

\(M=\frac{2}{30}+\frac{2}{42}+...+\frac{2}{1980}\)

\(M=2\left(\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{44.45}\right)\)

\(M=2\left(\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{44}-\frac{1}{45}\right)\)

\(M=2\left(\frac{1}{5}-\frac{1}{45}\right)\)

\(M=2\times\frac{8}{45}\)

\(M=\frac{16}{45}\)

18 tháng 5 2016

\(M=\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+....+\frac{1}{946}+\frac{1}{990}\)

\(M=\frac{2}{30}+\frac{2}{42}+\frac{2}{56}+.....+\frac{2}{1892}+\frac{2}{1980}\)

\(M=2.\left(\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+...+\frac{1}{1892}+\frac{1}{1980}\right)\)

\(M=2.\left(\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+....+\frac{1}{43.44}+\frac{1}{44.45}\right)\)

\(M=2.\left(\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+....+\frac{1}{43}-\frac{1}{44}+\frac{1}{44}-\frac{1}{45}\right)\)

\(M=2.\left(\frac{1}{5}-\frac{1}{45}\right)=2.\frac{8}{45}=\frac{16}{45}\)

Vậy M=16/45

9 tháng 2 2018

Đặt tổng trên = A

Có : A = 1/1.2.3 + 1/2.3.4 + ...... + 1/9.10.11

2A = 2/1.2.3 + 2/2.3.4 + ...... + 2/9.10.11

     = 1/1.2 - 1/2.3 + 1/2.3 - 1/3.4 + ....... + 1/9.10 - 1/10.11

     = 1/1.2 - 1/10.11

     = 1/2 - 1/110 = 27/55

=> A = 27/55 : 2 = 27/110

Tk mk nha

26 tháng 2 2020

\(\frac{-5}{x}=\frac{-y}{8}=\frac{18}{72}\)

\(\Leftrightarrow\frac{-5}{x}=\frac{-y}{8}=\frac{1}{4}\)

\(\Leftrightarrow\orbr{\begin{cases}-\frac{5}{x}=\frac{1}{4}\\-\frac{y}{8}=\frac{1}{4}\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-5.4:1\\-y=8.1:4\end{cases}\Leftrightarrow\orbr{\begin{cases}x=-20\\-y=2\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=-20\\y=-2\end{cases}}}\)

vậy x=-20 và y=-2

26 tháng 2 2020

\(-\frac{1}{3}-x=\frac{1}{2}-\frac{1}{-4}\)

\(-\frac{1}{3}-x=\frac{1}{2}-\frac{-1}{4}\)

\(-\frac{1}{3}-x=\frac{2}{4}-\frac{-1}{4}\)

\(-\frac{1}{3}-x=\frac{3}{4}\)

\(x=-\frac{1}{3}-\frac{3}{4}\)

\(x=-\frac{4}{12}-\frac{9}{12}\)

\(x=-\frac{13}{12}\)

19 tháng 5 2019

#)Trả lời :

 \(A=\frac{\left(140+70+42+28+20+15\right)}{420}\)

\(A=\frac{315}{420}=\frac{\left(315:105\right)}{\left(420:105\right)}=\frac{3}{4}\)

Vậy : \(A=\frac{3}{4}\)

         #~Will~be~Pens~#

19 tháng 5 2019

Tính nhanh mà cậu

28 tháng 3 2022

mong là trước ngày mai

28 tháng 3 2022

`Answer:`

Bài 1:

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

\(\Leftrightarrow\frac{1}{2}-\frac{2}{3}x+\frac{1}{3}=\frac{2}{3}\)

\(\Leftrightarrow\frac{5}{6}-\frac{2}{3}x=\frac{2}{3}\)

\(\Leftrightarrow-\frac{2}{3}=\frac{2}{3}-\frac{5}{6}\)

\(\Leftrightarrow-\frac{2}{3}x=-\frac{1}{6}\)

\(\Leftrightarrow x=-\frac{1}{6}:-\frac{2}{3}\)

\(\Leftrightarrow x=\frac{1}{4}\)

b. \(\frac{3}{x+5}=15\%\left(ĐKXĐ:x\ne-5\right)\)

\(\Leftrightarrow\frac{3}{x+5}=\frac{3}{20}\)

\(\Leftrightarrow\frac{60}{20\left(x+5\right)}=\frac{3\left(x+5\right)}{20\left(x+5\right)}\)

\(\Leftrightarrow60x=3x+15\)

\(\Leftrightarrow-3x=-45\)

\(\Leftrightarrow x=15\)

Bài 2:

\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\)

\(=1-\frac{1}{50}\)

\(=\frac{49}{50}\)

7 tháng 5 2019

\(A=\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+...+\frac{1}{49\cdot51}\)

\(\Rightarrow A=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{49}-\frac{1}{51}\)

\(\Rightarrow A=\frac{1}{3}-\frac{1}{51}=\frac{17}{51}-\frac{1}{51}=\frac{16}{51}\)

\(B=5\cdot\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-...+\frac{1}{100}-\frac{1}{103}\right)\)

\(\Rightarrow B=5\cdot\left(1-\frac{1}{103}\right)=5\cdot\frac{102}{103}=\frac{510}{103}\)

\(C=5\cdot\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{101}\right)\)

\(\Rightarrow C=5\cdot\left(1-\frac{1}{101}\right)=5\cdot\frac{100}{101}=\frac{500}{101}\)

7 tháng 5 2019

\(B=\frac{5}{1.4}+\frac{5}{4.7}+...+\frac{5}{100.103}\)

\(B=\frac{5}{3}\left(\frac{3}{1.4}+\frac{3}{4.7}+...+\frac{3}{100.103}\right)\)

\(B=\frac{5}{3}\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{100}-\frac{1}{103}\right)\)

\(B=\frac{5}{3}\left(1-\frac{1}{103}\right)\)

\(B=\frac{5}{3}.\frac{102}{103}=\frac{170}{103}\)

\(C=\frac{5}{1.3}+\frac{5}{3.5}+\frac{5}{5.7}+...+\frac{5}{99.101}\)

\(C=\frac{5}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{99.101}\right)\)

\(C=\frac{5}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{99}-\frac{1}{101}\right)\)

\(C=\frac{5}{2}\left(1-\frac{1}{101}\right)\)

\(C=\frac{5}{2}.\frac{100}{101}=\frac{250}{101}\)