\(\frac{7}{9}\)+\(\frac{7}{45}+\frac{7}{105}+...+\frac{...">
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19 tháng 7 2017

\(A=\frac{7}{9}+\frac{7}{45}+\frac{7}{105}+...+\frac{7}{27645}\)

\(=7\left(\frac{1}{9}+\frac{1}{45}+\frac{1}{105}+...+\frac{1}{27645}\right)\)

\(=7.\frac{1}{3}\left(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+...+\frac{1}{9215}\right)\)

\(=\frac{7}{3}\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{95.97}\right)\)

Đặt \(S=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{95.97}\)

\(2S=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{95.97}\)

\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{95}-\frac{1}{97}\)

\(=1-\frac{1}{97}=\frac{96}{97}\)

\(\Rightarrow S=\frac{96}{97}:2=\frac{96}{97.2}=\frac{48}{97}\). Thay vào \(A\) ta có:

\(A=\frac{7}{3}.\frac{48}{97}=\frac{112}{97}\)

Vậy \(A=\frac{112}{97}\).

14 tháng 4 2019

cảm ơn các bạn nào đã giúp mk nhé

14 tháng 4 2019

\(a)15\frac{3}{13}-\left(3\frac{4}{7}+8\frac{3}{13}\right)\)

\(=15\frac{3}{13}-3\frac{4}{7}-8\frac{3}{13}\)

\(=15\frac{3}{13}-8\frac{3}{13}-3\frac{4}{7}\)

\(=7-3\frac{4}{7}\)

\(=6\frac{7}{7}-3\frac{4}{7}=3\frac{3}{7}\)

\(b)\left(7\frac{4}{9}+4\frac{7}{11}\right)-3\frac{4}{9}\)

\(=7\frac{4}{9}-4\frac{7}{11}-3\frac{4}{9}\)

\(=7\frac{4}{9}-3\frac{4}{9}-4\frac{7}{11}\)

\(=4-4\frac{7}{11}=\frac{7}{11}\)

\(M=\frac{\left(-7\right).15.9.15.14}{9.49.7.15}=\frac{-15.2}{7}=\frac{-30}{7}.\)

\(N=\frac{200}{189}+\frac{1}{14}=\)1.12962962963

11 tháng 4 2019

\(M=\left(\frac{-7}{9}\cdot\frac{9}{7}\right)\cdot\left(\frac{15}{49}\cdot\frac{14}{15}\right)\cdot15\)

\(M=\left(-1\right)\cdot\frac{2}{7}\cdot15\)

\(M=\frac{-30}{7}\)

\(N=\frac{5}{9}\cdot\frac{4}{7}\cdot\frac{10}{3}+\frac{3}{9}\cdot\frac{3}{7}\cdot\frac{1}{2}\)

\(N=\frac{200\cdot2}{189\cdot2}+\frac{9\cdot3}{126\cdot3}\)

\(N=\frac{400}{378}+\frac{27}{378}\)

\(N=\frac{61}{51}\)

T i ck nha

18 tháng 4 2019

\(-1\frac{5}{7}.15+\frac{2}{7}.\left(-15\right)+\left(-105\right).\left(\frac{2}{7}-\frac{4}{5}+\frac{1}{7}\right)\)

\(=\frac{-12}{7}.15+\frac{2}{7}.\left(-15\right)+\left(-105\right).\left(\frac{-13}{35}\right)\)

\(=\left(\frac{-12}{7}+\frac{-2}{7}\right).15+39\)

\(=\left(-2\right).15+39\)

\(=\left(-30\right)+39\)

\(=9\)

6 tháng 6 2016

e) \(E=0,7.2\frac{2}{3}.20.0,375.\frac{5}{28}\)

        \(=\left(0,7.20\right)\left(2\frac{2}{3}.0,375\right)\frac{5}{28}\)

        \(=14.1.\frac{5}{28}\)

        \(=14.\frac{5}{28}\)

        \(=\frac{5}{2}\)

f) \(F=\left(9,75.21\frac{3}{7}+\frac{39}{4}.18\frac{4}{7}\right)\frac{15}{78}\)

       \(=\left(\frac{39}{4}.21\frac{3}{7}+\frac{39}{4}.18\frac{4}{7}\right)\frac{15}{78}\)

       \(=\frac{39}{4}\left(21\frac{3}{7}+18\frac{4}{7}\right)\frac{15}{78}\)

       \(=\frac{39}{4}.40.\frac{15}{78}\)

       \(=390.\frac{15}{78}\)

       \(=78\)

Chúc bạn học tốt môn Toán!!!

6 tháng 6 2016

Mình ko ghi đề đâu

\(A=49\frac{8}{23}-5\frac{7}{32}-14\frac{8}{23}=\left(49\frac{8}{23}-14\frac{8}{23}\right)-5\frac{7}{32}=35-5\frac{7}{32}=29\frac{25}{32}\)

\(B=71\frac{38}{45}-43\frac{8}{45}+1\frac{17}{57}=\left(71\frac{38}{45}-43\frac{8}{45}\right)+1\frac{17}{57}=28\frac{2}{3}+1\frac{17}{57}=29\frac{55}{57}\)

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

29 tháng 7 2019

a) \(A=\frac{-7}{813}+496.\left(\frac{-7}{813}\right)+\left(\frac{-7}{813}\right).316\)

\(=\frac{-7}{813}.\left(1+496+316\right)\)

\(=\frac{-7}{813}.813\)

\(=-7\)

b) \(B=\frac{-9}{10}.\frac{5}{14}+\frac{1}{10}.\left(\frac{-9}{2}\right)+\frac{1}{7}.\left(\frac{-9}{10}\right)\)

\(=\frac{-9}{10}.\left(\frac{5}{14}+\frac{1}{2}+\frac{1}{7}\right)\)

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

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

21 tháng 7 2018

a)   \(\frac{31}{23}-\left(\frac{7}{32}+\frac{8}{23}\right)=\frac{31}{23}-\frac{7}{32}-\frac{8}{23}=1-\frac{7}{32}=\frac{25}{32}\)

b)   \(\left(\frac{1}{3}+\frac{12}{67}+\frac{13}{41}\right)-\left(\frac{79}{67}-\frac{28}{41}\right)\)

\(=\frac{1}{3}+\frac{12}{67}+\frac{13}{41}-\frac{79}{67}+\frac{28}{41}\)

\(=\frac{1}{3}-\left(\frac{79}{67}-\frac{12}{67}\right)+\left(\frac{13}{41}+\frac{28}{41}\right)\)

\(=\frac{1}{3}-1+1=\frac{1}{3}\)

d)   \(\frac{1}{7}.\frac{1}{3}+\frac{1}{7}.\frac{-1}{3}+\frac{17}{19}=\frac{1}{7}.\left(\frac{1}{3}-\frac{1}{3}\right)+\frac{17}{19}=\frac{17}{19}\)

e)  \(\frac{3}{5}.\frac{7}{9}+\frac{7}{5}.\frac{2}{9}=\frac{7}{5}.\left(\frac{3}{9}+\frac{2}{9}\right)=\frac{7}{5}.\frac{5}{9}=\frac{7}{9}\)

30 tháng 4 2018

a)\(=\frac{-3}{7}+\frac{15}{26}-\frac{2}{13}+\frac{3}{7}\)

\(=\left(\frac{-3}{7}+\frac{3}{7}\right)-\left(\frac{15}{26}+\frac{2}{13}\right)\)

\(=0-\frac{19}{26}\)

\(=-\frac{19}{26}\)

30 tháng 4 2018

c)\(=\frac{-11}{23}.\left(\frac{6}{7}+\frac{8}{7}\right)-\frac{1}{23}\)

\(=\frac{-11}{23}.2-\frac{1}{23}\)

\(=\frac{-22}{23}-\frac{1}{23}\)

\(=-1\)