\(\frac{1}{3}\)+\(\frac{1}{3^2}\)+\(\f...">
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10 tháng 7 2017

Ta có : \(A=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+.....+\frac{1}{3^{100}}\)

\(3A=1+\frac{1}{3}+\frac{1}{3^2}+......+\frac{1}{3^{99}}\)

\(\Rightarrow3A-A=1-\frac{1}{3^{100}}\)

\(\Rightarrow2A=1-\frac{1}{3^{100}}\)

\(\Rightarrow A=\frac{1-\frac{1}{3^{100}}}{2}\)

10 tháng 9 2020

giúp mik vs, mik bik các pạn giờ này đang ngủ rùi nhưng giúp mik lần này thui.yêu các pạn nhìu

12 tháng 9 2020

\(5\frac{1}{2}+\left(-3\right)=\frac{11}{2}+\frac{-3}{1}\)\(=\frac{11}{2}+\frac{-6}{2}=\frac{5}{2}\)\(;\)

\(4\frac{9}{11}+\left(-2\frac{1}{11}\right)=\frac{53}{11}+\frac{-23}{11}\)\(=\frac{30}{11}\)\(;\)

\(2\frac{1}{2}+\left(-6\right)=\frac{5}{2}+\frac{-6}{1}\)\(=\frac{5}{2}+\frac{-12}{2}=\frac{-7}{2}\)\(;\)

\(\left(-\frac{4}{5}\right)+\frac{1}{2}=\frac{-4}{5}+\frac{1}{2}\)\(=\frac{-8}{10}+\frac{5}{10}=\frac{-3}{10}\)\(;\)

\(4,3-\left(-1,2\right)=4,3+1,2=5,5\)\(=\frac{55}{10}=\frac{11}{2}\)\(;\)

\(0-\left(-0,4\right)=0+0,4=0,4\)\(=\frac{4}{10}=\frac{2}{5}\)\(;\)

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

\(\frac{-1}{2}-\frac{-1}{6}=\frac{-1}{2}+\frac{1}{6}\)\(=\frac{-3}{6}+\frac{1}{6}=\frac{-2}{6}=\frac{-1}{3}\)\(;\)

\(x+\frac{1}{3}=\frac{3}{4}\)                                \(;\)               \(x-\frac{2}{5}=\frac{5}{7}\)            \(;\)      

    \(x=\frac{3}{4}-\frac{1}{3}\)                                                             \(x=\frac{5}{7}+\frac{2}{5}\)

    \(x=\frac{5}{12}\)                                                                        \(x=\frac{39}{35}\)

\(-x-\frac{2}{3}=-\frac{6}{7}\)                                \(;\)               \(\frac{4}{7}-x=\frac{1}{3}\)

 \(\frac{6}{7}-\frac{2}{3}=x\)                                                          \(\frac{4}{7}-\frac{1}{3}=x\)

            \(\frac{4}{21}=x\) \(\Leftrightarrow\)\(x=\frac{4}{21}\)                                                       \(\frac{5}{21}=x\)\(\Leftrightarrow\)\(x=\frac{5}{12}\)

3 tháng 8 2018

\(2A=1+\frac{1}{2}+...+\frac{1}{2^{49}}\)

\(2A-A=1-\frac{1}{2^{50}}\)

\(A=1-\frac{1}{2^{50}}\)=> A bé hơn 1

tương tự nha

3 tháng 8 2018

\(A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{49}}+\frac{1}{2^{50}}\)

\(2A=2.\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{49}}+\frac{1}{2^{50}}\right)\)

\(2A=1+\frac{1}{2}+\frac{1}{2^2}+....+\frac{1}{2^{48}}+\frac{1}{2^{49}}\)

\(2A-A=\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{48}}+\frac{1}{2^{49}}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{49}}+\frac{1}{2^{50}}\right)\)

\(A=1-\frac{1}{2^{50}}< 1\)

    

20 tháng 6 2017

a, \(C=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{99}}\)

\(3C=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{98}}\)

\(3C-C=\left(1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{98}}\right)-\left(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{99}}\right)\)

\(2C=1-\frac{1}{3^{99}}\)

\(C=\frac{1}{2}-\frac{1}{2.3^{99}}< \frac{1}{2}\)(đpcm)

b, Đặt \(A=\frac{1}{3}+\frac{2}{3^2}+\frac{3}{3^3}+...+\frac{100}{3^{100}}\)

\(3A=1+\frac{2}{3}+\frac{3}{3^2}+...+\frac{100}{3^{99}}\)

\(3A-A=\left(1+\frac{2}{3}+\frac{3}{3^2}+...+\frac{100}{3^{99}}\right)-\left(\frac{1}{3}+\frac{2}{3^2}+\frac{3}{3^3}+...+\frac{100}{3^{100}}\right)\)

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

\(6A=3+1+\frac{1}{3}+...+\frac{1}{3^{98}}-\frac{100}{3^{99}}\)

\(6A-2A=\left(3+1+\frac{1}{3}+...+\frac{1}{3^{98}}-\frac{100}{3^{99}}\right)-\left(1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{99}}-\frac{100}{3^{100}}\right)\)

\(4A=3-\frac{100}{3^{99}}-\frac{1}{3^{99}}+\frac{100}{3^{100}}\)

\(4A=3-\frac{300}{3^{100}}-\frac{3}{3^{100}}+\frac{100}{3^{100}}\)

\(4A=3-\frac{397}{3^{100}}\)

\(A=\frac{3}{4}-\frac{397}{4.3^{100}}< \frac{3}{4}\)(đpcm)

13 tháng 9 2020

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

=> \(3x-\frac{3}{2}-3x+1=x\)

=> \(x=-\frac{1}{2}\)

2) \(\frac{1}{3}x+5-x=\frac{1}{2}-2x\)

=> \(\frac{1}{3}x-x+2x=-5+\frac{1}{2}\)

=> \(\frac{4}{3}x=-\frac{9}{2}\)

=> x = \(-\frac{27}{8}\)

17 tháng 2 2018

1) \(+2x+3y⋮17\)

\(\Rightarrow26x+39y⋮17\)

\(\Rightarrow\left(9x+5y\right)+17x+34y⋮17\)

Mà \(17x+34y⋮17\)

\(\Rightarrow9x+5y⋮17\)

\(+9x+5y⋮17\)

\(\Rightarrow36x+20y⋮17\)

\(\Rightarrow\left(2x+3y\right)+34x+17y⋮17\)

Mà \(34x+17y⋮17\)

\(\Rightarrow2x+3y⋮17\)

21 tháng 8 2019

\(x+\left(\frac{1}{2}\right)^3=\frac{1}{4}\)

\(x+\frac{1}{8}=\frac{1}{4}\)

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

\(x=\frac{4}{16}-\frac{2}{16}\)

\(x=\frac{1}{8}\)

Vậy \(x=\frac{1}{8}\)

b) \(\left(\frac{2}{3}\right)^3-x=\frac{1}{3}\)

      \(\frac{8}{27}-x=\frac{1}{3}\)

                    \(x=\frac{8}{27}-\frac{1}{3}\)

                    \(x=\frac{8}{27}-\frac{9}{27}\)

                     \(x=-\frac{1}{27}\)

Vậy \(x=-\frac{1}{27}\)

c) \(x.\left(-\frac{1}{2}\right)^4=\frac{3}{8}\)

 \(x.\frac{1}{16}=\frac{3}{8}\)

       \(x=\frac{3}{8}:\frac{1}{16}\)

        \(x=\frac{3}{8}.16\)

      \(x=6\)

c) \(\left(\frac{1}{2}\right)^3.x=\left(\frac{1}{2}\right)^5\)

\(x=\left(\frac{1}{2}\right)^5:\left(\frac{1}{2}\right)^3\)

\(x=\left(\frac{1}{2}\right)^2\)

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

Vậy \(x=\frac{1}{4}\)

Chúc bạn học tốt !!!

21 tháng 8 2019

a) \(x+\left(\frac{1}{2}\right)^3=\frac{1}{4}\Leftrightarrow x+\frac{1}{8}=\frac{1}{4}\Leftrightarrow x=\frac{1}{4}-\frac{1}{8}\Leftrightarrow x=\frac{1}{8}\)

b) \(\left(\frac{2}{3}\right)^3-x=\frac{1}{3}\Leftrightarrow\frac{8}{27}-x=\frac{1}{3}\Leftrightarrow-x=\frac{1}{3}-\frac{8}{27}\Leftrightarrow-x=\frac{1}{27}\Leftrightarrow x=-\frac{1}{27}\)

c) \(x.\left(\frac{-1}{2}\right)^4=\frac{3}{8}\Leftrightarrow x.\frac{1}{16}=\frac{3}{8}\Leftrightarrow x=\frac{3}{8}:\frac{1}{16}\Leftrightarrow x=6\)

d) \(\left(\frac{1}{2}\right)^2.x=\left(\frac{1}{2}\right)^5\Leftrightarrow\frac{1}{8}.x=\frac{1}{32}\Leftrightarrow x=\frac{1}{32}:\frac{1}{8}\Leftrightarrow x=\frac{1}{4}\)