1/18 + 1/36 + ... + 1/19700 = ?
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\(18+\dfrac{1}{11}\times\left(x-18\right)=36+\dfrac{1}{11}\times\left[\dfrac{10}{11}\times\left(x-18\right)-36\right]\)
\(\Leftrightarrow\dfrac{198}{11}+\dfrac{1}{11}\times\left(x-18\right)=36+\dfrac{1}{11}\times\left[\dfrac{10}{11}\times\left(x-18\right)-\dfrac{396}{11}\right]\)
\(\Leftrightarrow\dfrac{198+x-18}{11}=36+\dfrac{1}{11}\times\dfrac{10x-180-396}{11}\)
\(\Leftrightarrow\dfrac{180+x}{11}=36+\dfrac{10x-576}{121}\)
\(\Leftrightarrow\dfrac{1980+11x}{121}=\dfrac{4356}{121}+\dfrac{10x-576}{121}\)
\(\Leftrightarrow1980+11x=4356+10x-576\)
\(\Leftrightarrow11x-10x=4356-1980-576\)
\(\Leftrightarrow x=1800\)
A=1/18 + 1/36 + ... + 1/29700
A= 1/3.6 + 1/3.12 + ... 1/3.9900
A= 1/3 . 1/6 + 1/3 . 1/12 + ... + 1/3 . 1/9900
A= 1/3 .(1/2.3 +1/3.4 + ... + 1/99.100)
A= 1/3 .(1/2 - 1/3 +1/3 -1/4 + ... + 1/99 - 1/100)
A= 1/3 .(1/2 - 1/100)
A= 1/3 . 49/100
A= 49/300
câu a :
\(\dfrac{1}{8}+\dfrac{3}{4}=\dfrac{7}{8}\)
câu b :
\(\dfrac{1}{36}+\dfrac{5}{12}=\dfrac{4}{9}\)
câu c :
\(\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{18}=\dfrac{5}{9}\)
\(\dfrac{1}{8}+\dfrac{3}{4}=\dfrac{1}{8}+\dfrac{6}{8}=\dfrac{1+6}{8}=\dfrac{7}{8}\)
\(\dfrac{1}{36}+\dfrac{5}{12}=\dfrac{1}{36}+\dfrac{15}{36}=\dfrac{1+15}{36}=\dfrac{16}{36}=\dfrac{4}{9}\)
\(\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{18}=\dfrac{6}{18}+\dfrac{3}{18}+\dfrac{1}{18}=\dfrac{6+3+1}{18}=\dfrac{10}{18}=\dfrac{5}{9}\)
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CHO MÌNH CÁCH GIẢI VỚI Ạ BẠN MẶC THIÊN PHONG ƠI. MÌNH CẢM ƠN
\(\dfrac{6}{7}:\dfrac{18}{42}\times\left(\dfrac{1}{2}+36\times\dfrac{1}{8}\right)\\ =\dfrac{6}{7}:\dfrac{18}{42}\times\left(\dfrac{1}{2}+\dfrac{9}{2}\right)\\ =\dfrac{6}{7}:\dfrac{18}{42}\times5\\ =10\)