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Ta có:\(\frac{1}{10}+\frac{1}{40}+\frac{1}{88}+....+\frac{1}{340}=\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+...+\frac{1}{17.20}\)
= \(\frac{1}{3}\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+.....+\frac{1}{17}-\frac{1}{20}\right)=\frac{1}{3}.\left(\frac{1}{2}-\frac{1}{20}\right)=\frac{1}{3}.\frac{9}{20}=\frac{3}{20}\)
Ta có :
\(N=\frac{1}{10}+\frac{1}{40}+\frac{1}{88}+\frac{1}{154}+\frac{1}{238}+\frac{1}{340}\)
\(N=\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+\frac{1}{11.14}+\frac{1}{14.17}+\frac{1}{17.20}\)
\(3N=\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}+\frac{3}{14.17}+\frac{3}{17.20}\)
\(3N=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}+\frac{1}{17}-\frac{1}{20}\)
\(3N=\frac{1}{2}-\frac{1}{20}\)
\(3N=\frac{9}{20}\)
\(N=\frac{9}{20}:3\)
\(N=\frac{3}{20}\)
Vậy \(N=\frac{3}{20}\)
Chúc bạn học tốt ~
\(N=\frac{1}{10}+\frac{1}{40}+...+\frac{1}{238}+\frac{1}{340}\)
\(N=\frac{1}{2.5}+\frac{1}{5.8}+...+\frac{1}{14.17}+\frac{1}{17.20}\)
\(N=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{14}-\frac{1}{17}+\frac{1}{17}-\frac{1}{20}\)
\(N=\frac{1}{2}-\frac{1}{20}\)
\(N=\frac{10}{20}-\frac{1}{20}\)
\(N=\frac{9}{20}\)
\(80-\frac{1}{9}-\frac{2}{10}-\frac{3}{11}-...-\frac{80}{88}=\left(1-\frac{1}{9}\right)+\left(1-\frac{2}{10}\right)+\left(1-\frac{3}{11}\right)+...+\left(1-\frac{80}{88}\right)\)
\(=\frac{8}{9}+\frac{8}{10}+\frac{8}{11}+...+\frac{8}{88}=8.\left(\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+\frac{1}{88}\right)\)
\(\frac{1}{45}+\frac{1}{50}+\frac{1}{55}+...+\frac{1}{440}=\frac{1}{5}\left(\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+...+\frac{1}{88}\right)\)
=>B=8:1/5=40
Ta có:
\(A=\left(x-\frac{1}{2}\right).\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{90}\right)=\frac{1}{3}\)
\(\Leftrightarrow A=\left(x-\frac{1}{2}\right).\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{9.10}\right)=\frac{1}{3}\)
\(\Leftrightarrow A=\left(x-\frac{1}{2}\right).\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{10}\right)=\frac{1}{3}\)
\(\Leftrightarrow A=\left(x-\frac{1}{2}\right).\left(\frac{1}{1}-\frac{1}{10}\right)=\frac{1}{3}\)
\(\Leftrightarrow A=\left(x-\frac{1}{2}\right).\frac{9}{10}=\frac{1}{3}\Leftrightarrow x-\frac{1}{2}=\frac{1}{3}.\frac{10}{9}\Leftrightarrow x=\frac{47}{54}\)
\(B=\frac{1}{1.6}+\frac{1}{6.11}+\frac{1}{11.16}+...+\frac{1}{96.101}=\frac{1}{10.x}\)
\(\Leftrightarrow B=\frac{1}{5}.\left(\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+...+\frac{5}{96.101}\right)=\frac{1}{10}-\frac{1}{x}\)
\(\Leftrightarrow B=\frac{1}{5}.\left(\frac{1}{1}-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{96}-\frac{1}{101}\right)=\frac{1}{10}-\frac{1}{x}\)
\(\Leftrightarrow B=\frac{1}{5}.\left(\frac{1}{1}-\frac{1}{101}\right)=\frac{1}{10}-\frac{1}{x}\Leftrightarrow B=\frac{1}{5}.\frac{100}{101}=\frac{1}{10}-\frac{1}{x}\)
\(\Leftrightarrow B=\frac{1}{x}=\frac{1}{10}-\frac{20}{101}=-\frac{99}{1010}\Leftrightarrow x=-\frac{1010}{99}\)
c) Sai đề nhé bạn vì không có kết quả nên không tìm được x.
d) \(\left(x-5\right).\left(10-9\frac{40}{41}\right):\left(1-\frac{81}{82}\right):\left(1-\frac{204}{205}\right)=2050\)
\(\Rightarrow\left(x-5\right).\frac{1}{41}.82.205=2050\)
\(\Rightarrow\left(x-5\right).2.205=2050\Leftrightarrow x-5=2050:410=5\Leftrightarrow x=10\)
A=1/3x(1/2x5+1/5x8+......+1/20x23)
A=1/3x(1/2-1/5+1/5-1/8+......+1/20-1/23)
A=1/3x(1/2-1/23)
A=1/3x21/46
A=7/46
=(5/30+3/30+2/30) : (5/30+3/30-2/30)
=10/30 : 5/30
=10/30 x 30/5
=2
!!! Hok tốt!!!
\(\left(\frac{1}{6}+\frac{1}{10}+\frac{1}{15}\right):\left(\frac{1}{6}+\frac{1}{10}-\frac{1}{15}\right)\)
=\(\frac{10}{30}:\frac{6}{30}\)
\(=\frac{5}{3}\)
\(\Rightarrow\left[\frac{1}{2\times5}+\frac{1}{5\times8}+...+\frac{1}{17\times20}\right]\cdot\frac{2x}{10}\)
\(\Rightarrow\left[\frac{1}{3}\left[\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{17}-\frac{1}{20}\right]\right]\cdot20=\frac{2x}{10}\)
\(\Rightarrow\left[\frac{1}{3}\left[\frac{1}{2}-\frac{1}{20}\right]\right]\cdot20=\frac{2x}{10}\)
\(\Rightarrow\left[\frac{1}{3}\cdot\frac{9}{20}\right]\cdot20=\frac{2x}{10}\)
\(\Rightarrow\frac{3}{20}\cdot20=\frac{2x}{10}\)
\(\Rightarrow3\cdot20=\frac{2x}{10}\Leftrightarrow60=\frac{2x}{10}\)
=> 2x = 60*10
=> 2x = 600
=> x = 300
\(\left(\frac{1}{10}+\frac{1}{40}+\frac{1}{88}+...+\frac{1}{340}\right).20=\frac{2x}{10}\)
\(\left(\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+...+\frac{1}{17.20}\right).20=\frac{2x}{10}\)
\(\left[3.\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{17}-\frac{1}{20}\right)\right].20=\frac{2x}{10}\)
\(\left[3.\left(\frac{1}{2}-\frac{1}{20}\right)\right].20=\frac{2x}{10}\)
\(\left(3.\frac{9}{20}\right).20=\frac{2x}{10}\)
\(\frac{27}{20}.20=2x\div10\)
\(27=2x\div10\)
\(x=27\times10\div2\)
\(\Rightarrow x=135\)