\(A=\frac{1}{1.6}+\frac{1}{3.10}+\frac{1}{5.14}+...+\frac{1}{41.86}\)

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30 tháng 6 2020

\(A=\frac{1}{1.2.3}+\frac{1}{3.2.5}+\frac{1}{5.2.7}+\frac{1}{7.2.9}+...+\frac{1}{41.2.43}\)

\(4A=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{41.43}\)

\(4A=\frac{3-1}{1.3}+\frac{5-3}{3.5}+\frac{7-5}{5.7}+\frac{9-7}{7.9}+...+\frac{43-41}{41.43}\)

\(4A=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{41}-\frac{1}{43}=1-\frac{1}{43}\)

\(A=\frac{1}{4}-\frac{1}{172}=\frac{42}{172}=\frac{21}{86}\)

22 tháng 6 2020

A=1/1.6+1/3.10+1/5.14+..........+1/41.86

A=1/2(1/1.3+1/3.5+1/5.7+.............+1/41.43)

A=1/2(1-1/3+1/3-1/5+1/5-1/7+..............+1/41-1/43)

A=1/2(1-1/43)

A=1/2*42/43=21/43

HỌC TỐT NHÉ!!!

24 tháng 6 2020

sai rồi

5 tháng 4 2018

bài 1.a)\(A=\frac{9^3.25^3}{18^2.125^2}=\frac{3^6.5^6}{2^2.3^4.5^6}=\frac{9}{4}\)

b) \(B=\frac{18}{37}+\frac{19}{37}+\frac{8}{2017}-\frac{4026}{2017}+\frac{2017}{2018}\)

\(=1-\frac{4014}{2017}+\frac{2017}{2018}=\frac{1997}{2017}+\frac{2017}{2018}\)

5 tháng 7 2017

\(B=\frac{1}{1.2}+\frac{1}{2.3}+....+\frac{1}{9.10}\)

\(B=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+....++\frac{1}{9}-\frac{1}{10}\)

\(B=1-\frac{1}{10}=\frac{9}{10}\)

\(C=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{99.100}\)

\(C=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\)

\(C=1-\frac{1}{100}\)

\(C=\frac{99}{100}\)

5 tháng 7 2017

\(D=\frac{1}{1.6}+\frac{1}{6.11}+...+\frac{1}{496.501}\)

\(D=\frac{1}{5}\cdot\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+.....+\frac{1}{496}-\frac{1}{501}\right)\)

\(D=\frac{1}{5}\cdot\left(1-\frac{1}{501}\right)=\frac{1}{5}\cdot\frac{500}{501}=\frac{100}{501}\)

20 tháng 4 2018

\(A=\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+....+\frac{1}{496}-\frac{1}{501}\right):5\)

\(A=\left(1-\frac{1}{501}\right):5\)

\(A=\frac{500}{501}:5=\frac{100}{501}\)

Ta có : \(A=\frac{1}{1.6}+\frac{1}{6.11}+\frac{1}{11.16}+...+\frac{1}{496.501}\)

    \(\Rightarrow\)  \(A=\frac{1}{5}\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{496}-\frac{1}{501}\right) \)

     \(\Rightarrow\)  \(A=\frac{1}{5}\left(1-\frac{1}{501}\right)\)

      \(\Rightarrow\)  \(A=\frac{1}{5}.\frac{501-1}{501}=\frac{1}{5}.\frac{500}{501}\)

       \(\Rightarrow\)  \(A=\frac{1.500}{5.501}=\frac{20}{1.501}=\frac{20}{501}\)     

                                               Vậy   \(A=\frac{20}{501}\)

20 tháng 3 2017

a) 2A= 1+1/2^2+1/2^3+...+1/2^2015+1/2^2016

2A-A=(1+1/2+1/2^2+...+1/2^2015+1/2^2016)-(1/2+1/2^2+...+1/2^2016+1/2^2017)

A= 1-1/2^2017

b) B=5.(5/1.6+5/6.11+...+5/26.31)

B=5.(1/5-1/6+1/6-1/11+1/11...-1/26+1/26-1/31)

B= 5.(1/5-1/31)

B=5.26/155

B=26/31

19 tháng 3 2017

cần giải ko, đợi 1 chút 30p sau tôi giúp cho 

6 tháng 4 2019

\(S=\frac{5^2}{1.6}+\frac{5^2}{6.11}+...+\frac{5^2}{26.31}\)

\(S=5.\left(\frac{5}{1.6}+\frac{5}{6.11}+...+\frac{5}{26.31}\right)\)

\(S=5.\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{26}-\frac{1}{31}\right)\)

\(S=5.\left(1-\frac{1}{31}\right)\)

\(S=5.\frac{30}{31}\)

\(S=\frac{150}{31}\)

Câu L bạn thiếu số\(\frac{1}{475}\)

\(L=\frac{1}{7}+\frac{1}{91}+\frac{1}{247}+\frac{1}{475}+\frac{1}{775}+\frac{1}{1147}\)

\(L=\frac{1}{1.7}+\frac{1}{7.13}+\frac{1}{13.19}+\frac{1}{19.25}+\frac{1}{25.31}+\frac{1}{31.37}\)

\(L=\frac{1}{6}.\left(\frac{6}{1.7}+\frac{6}{7.13}+\frac{6}{13.19}+\frac{6}{19.25}+\frac{6}{25.31}+\frac{6}{31.37}\right)\)

\(L=\frac{1}{6}.\left(1-\frac{1}{7}+\frac{1}{7}-\frac{1}{13}+\frac{1}{13}-\frac{1}{19}+\frac{1}{19}-\frac{1}{25}+\frac{1}{25}-\frac{1}{31}+\frac{1}{31}-\frac{1}{37}\right)\)

\(L=\frac{1}{6}.\left(1-\frac{1}{37}\right)\)

\(L=\frac{1}{6}.\frac{36}{37}\)

\(L=\frac{6}{37}\)

6 tháng 4 2019

\(S=\frac{5^2}{1.6}+\frac{5^2}{6.11}+...+\frac{5^2}{26.31}\)

\(=5\left[\left(1-\frac{1}{6}\right)+\left(\frac{1}{6}-\frac{1}{11}\right)+...+\left(\frac{1}{26}-\frac{1}{31}\right)\right]\)

\(=5\left[1-\frac{1}{31}\right]\)

\(=5.\frac{30}{31}=\frac{150}{31}\)

\(L=\frac{1}{7}+\frac{1}{91}+\frac{1}{247}+\frac{1}{775}+\frac{1}{1147}\)

\(L.6=\frac{6}{1.7}+\frac{6}{7.13}+\frac{6}{13.19}+\frac{6}{19.25}+\frac{6}{25.31}\)

\(L.6=\left(1-\frac{1}{7}\right)+\left(\frac{1}{7}-\frac{1}{13}\right)+\left(\frac{1}{13}-\frac{1}{19}\right)+\left(\frac{1}{19}-\frac{1}{25}\right)+\left(\frac{1}{25}-\frac{1}{31}\right)\)

\(L.6=1-\frac{1}{31}\)

\(L.6=\frac{31}{31}-\frac{1}{31}\)

\(L.6=\frac{25}{31}\)

\(L=\frac{30}{31}:6\)

\(L=\frac{30}{31}.\frac{1}{6}\)

\(L=\frac{30}{186}\)