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15 tháng 2 2016

N=3(3/8.11 +3 /11.14 + 3/14.17 +...+3/197.200)

N=3( 1/8-1/11+1/11-1/14+1/14-1/17+...+1/197-1/200)

N=3(1/8-1/200)

N=3. 3/25=9/25

Ủng hộ mk nha

15 tháng 2 2016

\(\Rightarrow N=\frac{9}{8.11}+\frac{9}{11.14}+\frac{9}{14.17}+....+\frac{9}{197.200}\)

\(\Rightarrow N=\frac{9}{3}\left(\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+...+\frac{1}{197}-\frac{1}{200}\right)\)

\(\Rightarrow N=3\left(\frac{1}{8}-\frac{1}{200}\right)=\frac{3}{8}-\frac{3}{200}=\frac{75}{200}-\frac{3}{200}=\frac{72}{200}=\frac{9}{25}\)

17 tháng 4 2016

\(32\left(\frac{1}{8.11}+\frac{1}{11.14}+\frac{1}{14.17}+...+\frac{1}{197.200}\right)-x=\frac{1}{2}\)

\(\frac{32}{3}\left(\frac{3}{8.11}+\frac{3}{11.14}+\frac{3}{14.17}+....+\frac{3}{197.200}\right)-x=\frac{1}{2}\)

\(\frac{32}{3}\left(\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}+...+\frac{1}{197}-\frac{1}{200}\right)-x=\frac{1}{2}\)

\(\frac{32}{3}\left(\frac{1}{8}-\frac{1}{200}\right)-x=\frac{1}{2}\)

x=0.78

28 tháng 7 2021

\(\dfrac{3^2}{8.11}+\dfrac{3^2}{11.14}+...+\dfrac{3^2}{197.200}\)

=\(3.\left(\dfrac{3}{8.11}+\dfrac{3}{11.14}+...+\dfrac{3}{197.200}\right)\)

=\(3.\left(\dfrac{1}{8}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{14}+...+\dfrac{1}{197}-\dfrac{1}{200}\right)\)

=\(3.\left(\dfrac{1}{8}-\dfrac{1}{200}\right)\)

=\(3.\dfrac{3}{25}=\dfrac{9}{25}\)

 

\(B=\frac{9}{8\cdot11}+\frac{9}{11\cdot14}+...+\frac{9}{197\cdot200}\)

\(=3\left(\frac{3}{8\cdot11}+\frac{3}{11\cdot14}+...+\frac{3}{197\cdot200}\right)\)

\(=3\left(\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+...+\frac{1}{197}-\frac{1}{200}\right)\)

\(=3\left(\frac{1}{8}-\frac{1}{200}\right)\)

\(=3\left(\frac{24}{200}-\frac{1}{200}\right)\)

\(=3\cdot\frac{23}{200}\)

đúng

5 tháng 4 2019

Đặt 3 ra ngoài

18 tháng 3 2018

=1,798

18 tháng 3 2018

Ta có : 

\(C=\frac{3^2}{8.11}+\frac{3^2}{11.14}+\frac{3^2}{14.17}+...+\frac{3^2}{197.200}\)

\(C=3\left(\frac{3}{8.11}+\frac{3}{11.14}+\frac{3}{14.17}+...+\frac{3}{197.200}\right)\)

\(C=3\left(\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}+...+\frac{1}{197}-\frac{1}{200}\right)\)

\(C=3\left(\frac{1}{8}-\frac{1}{200}\right)\)

\(C=3.\frac{3}{25}\)

\(C=\frac{9}{25}\)

Chúc bạn học tốt ~ 

16 tháng 3 2017

kết quả bài nãy bằng kkkkk

26 tháng 2 2019

Đặt \(A=\frac{3^2}{8.11}+\frac{3^2}{11.14}+\frac{3^2}{14.17}+...+\frac{3^2}{197.200}\)

\(\Leftrightarrow A=\frac{9}{8.11}+\frac{9}{11.14}+\frac{9}{14.17}+...+\frac{9}{197.200}\)

\(\Leftrightarrow\frac{1}{3}A=\frac{3}{8.11}+\frac{3}{11.14}+\frac{3}{14.17}+...+\frac{3}{197.200}\)

\(\Leftrightarrow\frac{1}{3}A=\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{2}{17}+...+\frac{1}{197}-\frac{1}{200}\)​b

\(\Leftrightarrow\frac{1}{3}A=\frac{1}{8}-\frac{1}{200}\)

\(\Leftrightarrow\frac{1}{3}A=\frac{24}{200}\)

\(\Leftrightarrow A=\frac{24}{200}\times3\)

\(\Leftrightarrow A=\frac{72}{200}=\frac{9}{25}\)

26 tháng 2 2019

Thank

30 tháng 6 2017

\(\left[\frac{2000}{2000.2006}+\frac{2000}{2006.2012}+...+\frac{2000}{2492.2498}\right]\times\left[\frac{3^2}{8.11}+\frac{3^2}{11.14}+\frac{3^2}{14.17}+...+\frac{3^2}{197.200}\right]\)

\(=\left[\frac{2000}{6}\cdot\left(\frac{1}{2000}-\frac{1}{2006}+...+\frac{1}{2492}-\frac{1}{2498}\right)\right]\times\left[\frac{9}{8.11}+\frac{9}{11.14}+...+\frac{9}{197.200}\right]\)

\(=\left[\frac{2000}{6}\cdot\left(\frac{1}{2000}-\frac{1}{2498}\right)\right]\times\left[\frac{9}{3}\cdot\left(\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+..+\frac{1}{197}-\frac{1}{200}\right)\right]\)

\(=\left[\frac{2000}{6}\cdot\frac{498}{4996000}\right]\times\left[\frac{9}{3}\cdot\left(\frac{1}{8}-\frac{1}{200}\right)\right]\)

\(=\frac{83}{2498}\times\left[\frac{9}{3}\cdot\frac{3}{25}\right]\)

\(=\frac{83}{2498}\times\frac{9}{25}=\frac{747}{62450}\)