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\(\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\right)\div x=\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{32}\right)\)
\(\left(\frac{8}{16}+\frac{4}{16}+\frac{2}{16}+\frac{1}{16}\right)\div x=\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{11.12}\right)\)
\(\frac{15}{16}\div x=\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{11}-\frac{1}{12}\right)\)
\(\frac{15}{16}\div x=\left(\frac{1}{1}-\frac{1}{12}\right)\)
\(\frac{15}{16}\div x=\frac{11}{12}\)
\(x=\frac{15}{16}\div\frac{11}{12}\)
\(x=\frac{15}{16}\times\frac{12}{11}\)
\(\Rightarrow x=\frac{180}{176}=\frac{45}{44}\)
1/6 + 1/12 + 1/20 + 1/30 + 1/42 + ... + 1/90 + 1/110 = 1/2.3 + 1/3.4 + 1/4.5 + 1/5.6 + 1/6.7 + ... + 1/9.10 + 1/10.11 = 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 + ... + 1/9 - 1/10 + 1/10 - 1/11 = 1/2 - 1/11 = 9/22
\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{90}+\frac{1}{110}\)
=\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{9.10}+\frac{1}{10.11}\)
=\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}\)
=\(\frac{1}{2}-\frac{1}{11}\)
=\(\frac{9}{22}\)
\(\left(\times-\frac{1}{5}\right):\left(\frac{1}{2}+\frac{1}{6}+\cdot\cdot\cdot+\frac{1}{110}\right)=\frac{1}{5}\)
\(\Rightarrow\left(\times-\frac{1}{5}\right):\left(\frac{1}{1\times2}+\cdot\cdot\cdot+\frac{1}{10\times11}\right)=\frac{1}{5}\)
\(\Rightarrow\left(\times-\frac{1}{5}\right):\left(1-\frac{1}{2}+\cdot\cdot\cdot+\frac{1}{10}-\frac{1}{11}\right)=\frac{1}{5}\)
\(\Rightarrow\left(\times-\frac{1}{5}\right):\left(1-\frac{1}{11}\right)=\frac{1}{5}\)
\(\Rightarrow\left(\times-\frac{1}{5}\right):\frac{10}{11}=\frac{1}{5}\)
\(\Rightarrow\left(\times-\frac{1}{5}\right)=\frac{1}{5}\times\frac{10}{11}\)
\(\Rightarrow\times-\frac{1}{5}=\frac{2}{11}\)
\(\Rightarrow\times=\frac{2}{11}+\frac{1}{5}\)
\(\Rightarrow\times=\frac{21}{55}\)
\(\left(x-\frac{1}{5}\right):\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{110}\right)=\frac{1}{5}\)
\(\Rightarrow\left(x-\frac{1}{5}\right):\left(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{10\times11}\right)=\frac{1}{5}\)
\(\Rightarrow\left(x-\frac{1}{5}\right):\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{10}-\frac{1}{11}\right)=\frac{1}{5}\)
\(\Rightarrow\left(x-\frac{1}{5}\right):\left(1-\frac{1}{11}\right)=\frac{1}{5}\)
\(\Rightarrow\left(x-\frac{1}{5}\right):\frac{10}{11}=\frac{1}{5}\)
\(\Rightarrow x-\frac{1}{5}=\frac{1}{5}\times\frac{10}{11}\)
\(\Rightarrow x-\frac{1}{5}=\frac{2}{11}\)
\(\Rightarrow x=\frac{2}{11}+\frac{1}{5}\)
\(\Rightarrow x=\frac{21}{55}\)
Vậy \(x=\frac{21}{55}\)
\(\frac{1}{12}\)+\(\frac{1}{20}\)+1/30+1/42+1/56+1/72+1/90+1/110+1/132
=\(\frac{1}{3\cdot4}\)+\(\frac{1}{4.5}\)+1/5x6+1/6x7+1/7x8+1/8x9+...1/11x12
=1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10+1/10-1/11+1/11-1/12
=1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10+1/10-1/11+1/11--1/12
=1/3-1/12
=1/4
Xin lỗi bạn nhé!vì trưa rồi nên mình làm vậy cho nhanh thôi!hjhj!
Nếu thấy mình làm đúng thì k mình nha!Thanks các bạn nhìu!
=1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10+1/10-1/11+1/11+1/12
=1/3-1/12
=4/12-1/12
=3/12
=1/4
=\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+.....+\frac{1}{110}\)
=\(\frac{1}{1.2}+\frac{1}{2\cdot3}+\frac{1}{3.4}+......+\frac{1}{10.11}\)
=\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+.......+\frac{1}{10}-\frac{1}{11}\)
=\(1-\frac{1}{11}\)
=\(\frac{10}{11}\)
\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{42}+...+\frac{1}{110}\)
\(=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+...+\frac{1}{10\cdot11}\)
\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{10}-\frac{1}{11}\)
\(=1-\frac{1}{11}\)
\(=\frac{10}{11}\)
A = 1/2 + 1/6 + 1/12 + .. + 1/110
A = 1/1 x 2 + 1/ 2 x 3 + 1/3 x 4 + ... + 1/10 x 11
A = 1/1 - 1/2 + 1/2 -1/3 + 13 - 1/4 + ... + 1/10 - 1/11
A = 1/1 -1/10
A = 10/10 - 1/10
A = 9/10
A=1/2+1/6+1/12+...+1/110
A=1/1.2+1/2.3+1/3.4+....+1/10.11
A=1-1/2+1/2-1/3+1/3-1/4+....+1/10-1/11
A=1-1/11
A=10/11
+ \(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+\frac{1}{8}\)
=> \(2A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}\)
=> \(A=2A-A=1-\frac{1}{16}=\frac{15}{16}\)
+ \(B=\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+...+\frac{1}{11x12}\)
\(B=\frac{2-1}{1x2}+\frac{3-2}{2x3}+\frac{4-3}{3x4}+...+\frac{12-11}{11x12}\)
\(B=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{11}-\frac{1}{12}\)
\(B=1-\frac{1}{12}=\frac{11}{12}\)
\(A:x=B\Rightarrow x=A:B=\frac{15}{16}:\frac{11}{12}=\frac{15}{16}x\frac{12}{11}=\frac{45}{44}=1\frac{1}{44}\)
\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{110}+\frac{1}{132}\)
= \(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+...+\frac{1}{10\times11}+\frac{1}{11\times12}\)
= \(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}\)
= \(\frac{1}{1}-\frac{1}{12}\)
= \(\frac{11}{12}\)
Ta có : \(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+......+\frac{1}{132}\)
\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+......+\frac{1}{11.12}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+......+\frac{1}{11}-\frac{1}{12}\)
\(=1-\frac{1}{12}\)
\(=\frac{11}{12}\)