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Đặt S = \(\frac{1}{7^2}+\frac{1}{7^4}+\frac{1}{7^6}+...+\frac{1}{7^{100}}\)
=> 72S = 49S = \(1+\frac{1}{7^2}+\frac{1}{7^4}+...+\frac{1}{7^{98}}\)
=> 49S - S = \(\left(1+\frac{1}{7^2}+\frac{1}{7^4}+...+\frac{1}{7^{98}}\right)-\left(\frac{1}{7^2}+\frac{1}{7^4}+\frac{1}{7^6}+...+\frac{1}{7^{100}}\right)\)
=> 48S = \(1-\frac{1}{7^{100}}\)
=> \(S=\frac{1-\frac{1}{7^{100}}}{48}\)
Khi đó A = \(\left(\frac{1-\frac{1}{7^{100}}}{48}\right):\left(1-\frac{1}{7^{100}}\right)=\frac{1}{48}\)
\(-4\frac{1}{3}.\left(\frac{1}{2}-\frac{1}{6}\right)\le x\le-\frac{2}{3}.\left(\frac{1}{3}-\frac{1}{2}-\frac{3}{4}\right)\)
\(\Rightarrow-\frac{13}{3}.\left(\frac{3}{6}-\frac{1}{6}\right)\le x\le-\frac{2}{3}.\left(\frac{4}{12}-\frac{6}{12}-\frac{9}{12}\right)\)
\(\Rightarrow-\frac{13}{3}.\frac{2}{6}\le x\le-\frac{2}{3}.\frac{-11}{12}\)
\(\Rightarrow\frac{-13}{9}\le x\le\frac{11}{18}\)
\(\Rightarrow\frac{-26}{18}\le x\le\frac{11}{18}\)
=> -1,44444444444........... ≤ x ≤ 0,6111111111...........
Mà x ∈ Z
=> x ∈ { -1 ; 0 }
\(2a+3b+\frac{6}{a}+\frac{10}{b}=\left(\frac{3}{2}a+\frac{6}{a}\right)+\left(\frac{5}{2}b+\frac{10}{b}\right)+\frac{1}{2}\left(a+b\right)\)
\(\ge2\sqrt{\frac{3}{2}a.\frac{6}{a}}+2\sqrt{\frac{5}{2}b.\frac{10}{b}}+\frac{1}{2}.4=18\)
\(1)A=a\frac{1}{3}+a\frac{1}{4}-a\frac{1}{6}=a\left(\frac{1}{3}+\frac{1}{4}-\frac{1}{6}\right)=a\frac{5}{12}\)
Thay \(a=-\frac{3}{5}\) vào A,ta đc:
\(A=-\frac{3}{5}.\frac{5}{12}=-\frac{1}{4}\)
\(2)B=b\frac{5}{6}+b\frac{3}{4}-b\frac{1}{2}=b\left(\frac{5}{6}+\frac{3}{4}-\frac{1}{2}\right)=b\frac{13}{12}\)
Thay \(b=\frac{12}{13}\) vào B, ta đc: \(B=b\frac{13}{12}=\frac{12}{13}.\frac{13}{12}=1\)
Đặt S = \(\frac{1}{6}+\frac{1}{6^2}+\frac{1}{6^3}+...+\frac{1}{6^{100}}\)
=> 6S = \(1+\frac{1}{6}+\frac{1}{6^2}+...+\frac{1}{6^{99}}\)
=> 6S - S = \(\left(1+\frac{1}{6}+\frac{1}{6^2}+\frac{1}{6^3}+...+\frac{1}{6^{99}}\right)-\left(\frac{1}{6}+\frac{1}{6^2}+\frac{1}{6^3}+...+\frac{1}{6^{100}}\right)\)
=> \(5S=1-\frac{1}{6^{100}}\)
=> \(S=\frac{1-\frac{1}{6^{100}}}{5}\)
Khi đó A = \(\left(1-\frac{1}{6^{100}}\right):\left(\frac{1-\frac{1}{6^{100}}}{5}\right)=5\)
a)\(-\frac{2}{5}+\frac{2}{3}x+\frac{1}{6}x=-\frac{4}{5}\Leftrightarrow\frac{5}{6}x=-\frac{2}{5}\Leftrightarrow x=-\frac{12}{25}\)
Vậy nghiệm là x = -12/25
b)\(\frac{3}{2}x-\frac{2}{5}-\frac{2}{3}x=-\frac{4}{15}\Leftrightarrow\frac{5}{6}x=\frac{2}{15}\Leftrightarrow x=\frac{4}{25}\)
Vậy nghiệm là x = 4/25
c)\(\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}=\frac{x+1}{13}+\frac{x+1}{14}\)\(\Leftrightarrow\left(x+1\right)\left(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}\right)=0\)
\(\Leftrightarrow x+1=0\left(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}\ne0\right)\)\(\Leftrightarrow x=-1\)
Vậy nghiệm là x = -1
\(a)\frac{a}{b}\times4+\frac{1}{6}=\frac{17}{6}\)
\(\frac{a}{b}\times4\) \(=\frac{17}{6}-\frac{1}{6}\)
\(\frac{a}{b}\times4\) \(=\frac{8}{3}\)( Đây là kết quả khi rút gọn phân số 16/6 nha )
\(\frac{a}{b}\) \(=\frac{8}{3}\div4\)
\(\frac{a}{b}\) \(=\frac{8}{3}\times\frac{1}{4}\)
\(\frac{a}{b}\) \(=\frac{2}{3}\)
\(b)\frac{4}{5}\div\frac{a}{b}\times2=\frac{16}{5}\)
\(\frac{4}{5}\div\frac{a}{b}\) \(=\frac{16}{5}\div2\)
\(\frac{4}{5}\div\frac{a}{b}\) \(=\frac{16}{5}\times\frac{1}{2}\)
\(\frac{4}{5}\div\frac{a}{b}\) \(=\frac{8}{5}\)
\(\frac{a}{b}\) \(=\frac{4}{5}\div\frac{8}{5}\)
\(\frac{a}{b}\) \(=\frac{4}{5}\times\frac{5}{8}\)
\(\frac{a}{b}\) \(=\frac{1}{2}\)
Nếu có gì ko hiểu bạn cứ hỏi mik nha.
hiu hiu giúp mình zới