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\(E=\dfrac{98:\left(\dfrac{4}{5}\cdot\dfrac{5}{4}\right)}{\dfrac{16}{25}-\dfrac{1}{25}}+\dfrac{\left(\dfrac{27}{25}-\dfrac{2}{25}\right)\cdot\dfrac{7}{4}}{\left(\dfrac{59}{9}-\dfrac{13}{4}\right)\cdot\dfrac{36}{17}}\\ E=\dfrac{98}{\dfrac{3}{5}}+\dfrac{\dfrac{7}{4}}{\dfrac{119}{36}\cdot\dfrac{36}{17}}\\ E=\dfrac{490}{3}+\dfrac{\dfrac{7}{4}}{7}=\dfrac{490}{3}+\dfrac{1}{4}=\dfrac{1963}{12}\)
bạn ơi chỗ kia mik nhìn hơi loạn tí bạn giải thích giúp mik với
\(P=\dfrac{1}{3}-\left(\dfrac{1}{3}\right)^2+\left(\dfrac{1}{3}\right)^3-\left(\dfrac{1}{3}\right)^4+...+\left(\dfrac{1}{3}\right)^{19}-\left(\dfrac{1}{3}\right)^{20}\)
\(=\left(\dfrac{1}{3}-\left(\dfrac{1}{3}\right)^2\right)+\left(\left(\dfrac{1}{3}\right)^3-\left(\dfrac{1}{4}\right)^4\right)+...+\left(\left(\dfrac{1}{3}\right)^{19}-\left(\dfrac{1}{3}\right)^{20}\right)\)
\(=\dfrac{1}{3}.\dfrac{2}{3}+\left(\dfrac{1}{3}\right)^3.\dfrac{2}{3}+...+\left(\dfrac{1}{3}\right)^{19}.\dfrac{2}{3}\)
\(=\dfrac{2}{3}.\left[\dfrac{1}{3}+\left(\dfrac{1}{3}\right)^3+...+\left(\dfrac{1}{3}\right)^{19}\right]\)
\(\dfrac{a}{b}=\dfrac{c}{d}\Rightarrow\dfrac{a}{c}=\dfrac{b}{d}\)
\(\left\{{}\begin{matrix}\dfrac{a}{c}=\dfrac{b}{d}=\dfrac{a-b}{c-d}\\\dfrac{a}{c}=\dfrac{b}{d}\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}\left(\dfrac{a}{c}\right)^2=\dfrac{\left(a-b\right)^2}{\left(c-d\right)^2}\\\left(\dfrac{a}{c}\right)^2=\dfrac{ab}{cd}\end{matrix}\right.\)
\(\Rightarrow\dfrac{ab}{cd}=\dfrac{\left(a-b\right)^2}{\left(c-d\right)^2}\)
Sửa: CMR \(\dfrac{a^3+c^3+m^3}{b^3+d^3+n^3}=\left(\dfrac{a+c-m}{b+d-n}\right)^3\)
Đặt \(\dfrac{a}{b}=\dfrac{c}{d}=\dfrac{m}{n}=k\Rightarrow a=kb;c=kd;m=kn\)
\(\dfrac{a^3+c^3+m^3}{b^3+d^3+n^3}=\dfrac{k^3b^3+k^3d^3+k^3n^3}{b^3+d^3+n^3}=\dfrac{k^3\left(b^3+d^3+n^3\right)}{b^3+d^3+n^3}=k^3\)
\(\left(\dfrac{a+c-m}{b+d-m}\right)^3=\left(\dfrac{kb+kd-kn}{b+d-n}\right)^3=\left(\dfrac{k\left(b+d-n\right)}{b+d-n}\right)^3=k^3\)
\(\Rightarrow\dfrac{a^3+c^3+m^3}{b^3+d^3+n^3}=\left(\dfrac{a+c-m}{b+d-n}\right)^3\left(=k^3\right)\)
a) \(\left(1\dfrac{1}{2}\right)\left(1\dfrac{1}{3}\right)..............\left(1\dfrac{1}{100}\right)\)
\(=\dfrac{3}{2}.\dfrac{4}{3}....................\dfrac{101}{100}\)
\(=\dfrac{1}{2}.\dfrac{101}{1}=\dfrac{101}{2}\)
b) \(1\dfrac{1}{2}.1\dfrac{1}{3}.1\dfrac{1}{4}...................1\dfrac{1}{2007}\)
\(=\dfrac{3}{2}.\dfrac{4}{3}.\dfrac{5}{4}....................\dfrac{2008}{2007}\)
\(=\dfrac{1}{2}.\dfrac{2008}{1}=1004\)
c) \(1\dfrac{1}{2}.1\dfrac{1}{3}.....................1\dfrac{1}{2017}\)
\(=\dfrac{3}{2}.\dfrac{4}{3}..................\dfrac{2018}{2017}\)
\(=\dfrac{1}{2}.\dfrac{2018}{1}=1009\)
\(A=1-\dfrac{3}{4}+\left(\dfrac{3}{4}\right)^2-\left(\dfrac{3}{4}\right)^3+...+\left(\dfrac{3}{4}\right)^{2016}-\left(\dfrac{3}{4}\right)^{2017}\\ \Rightarrow\dfrac{3}{4}A=\dfrac{3}{4}-\left(\dfrac{3}{4}\right)^2+\left(\dfrac{3}{4}\right)^3-\left(\dfrac{3}{4}\right)^3+...+\left(\dfrac{3}{4}\right)^{2017}-\left(\dfrac{3}{4}\right)^{2018}\\ \Rightarrow\dfrac{7}{4}A=1-\left(\dfrac{3}{4}\right)^{2018}\notin Z\\ \Rightarrow A\notin Z\)
\(\dfrac{2}{3}A=\dfrac{2}{3}-\left(\dfrac{2}{3}\right)^2+\left(\dfrac{2}{3}\right)^3-...+\left(\dfrac{2}{3}\right)^{2019}-\left(\dfrac{2}{3}\right)^{2020}\)
=>\(\dfrac{5}{3}A=1-\left(\dfrac{2}{3}\right)^{2020}=1-\dfrac{2^{2020}}{3^{2020}}=\dfrac{3^{2020}-2^{2020}}{3^{2020}}\)
=>\(A=\dfrac{3^{2020}-2^{2020}}{3^{2020}}:\dfrac{5}{3}=\dfrac{3^{2020}-2^{2020}}{5\cdot3^{2019}}\) ko là số nguyên
\(B=\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+...+\dfrac{1}{3^{100}}\)
\(3B=1+\dfrac{1}{3}+\dfrac{1}{3^2}+...+\dfrac{1}{3^{99}}\)
\(\Rightarrow3B-B=1-\dfrac{1}{3^{100}}\)
\(\Rightarrow2B=1-\dfrac{1}{3^{100}}\)
\(0< \dfrac{1}{3^{100}}< 1\Rightarrow0< 1-\dfrac{1}{3^{100}}< 1\)
\(\Rightarrow0< 2B< 1\Rightarrow0< B< \dfrac{1}{2}\Rightarrow\) B không phải số nguyên