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16 tháng 5 2017
1.Ta có:1/2=1/1.2
1/6=1/2.3
1/12=1/3.4
........
=>1/2+1/6+1/12+1/20+1/30=1/1.2+1/2.3+1/3.4+1/4.5+1/5.6
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6
=1-1/6
=5/6
2.hinh nhu sai đe
1 tháng 6 2018
x + 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 = 1
x + 1/1*2 + 1/2*3 + 1/3*4 + 1/4*5 + 1/5*6 + 1/6*7 = 1
x + 1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 = 1
x + 1/1 - 1/7 = 1
x + 6/7 = 1
x = 1 - 6/7
x = 1/7
1 tháng 6 2018
x + 1/2 + 1/6 + 1/20 + 1/30 + 1/42 = 1
x + 65/84 = 1
x = 1 - 65/84
x = 19/84
NT
0
16 tháng 8 2018
a)\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}+x=\frac{3}{5}\)
\(\Rightarrow\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}+x=\frac{3}{5}\)
\(\Rightarrow\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}+x=\frac{3}{5}\)
\(\Rightarrow\frac{1}{2}-\frac{1}{10}+x=\frac{3}{5}\)
\(\Rightarrow\frac{2}{5}+x=\frac{3}{5}\)
\(\Rightarrow x=\frac{3}{5}-\frac{2}{5}=\frac{1}{5}\)
b)\(\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{13.15}+x=\frac{1}{3}\)
\(\Rightarrow\frac{2}{3}-\frac{2}{5}+\frac{2}{5}-\frac{2}{7}+...+\frac{2}{13}-\frac{2}{15}+x=\frac{1}{3}\)
\(\Rightarrow\frac{2}{3}-\frac{2}{15}+x=\frac{1}{3}\)
\(\Rightarrow\frac{8}{15}+x=\frac{1}{3}\)
\(\Rightarrow x=\frac{1}{3}-\frac{8}{15}=-\frac{1}{5}\)
c)\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{x\left(x+1\right)}=\frac{9}{10}\)
\(\Rightarrow\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}=\frac{9}{10}\)
\(\Rightarrow\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{9}{10}\)
\(\Rightarrow\frac{1}{1}-\frac{1}{x+1}=\frac{9}{10}\)
\(\Leftrightarrow\frac{x+1-1}{x+1}=\frac{9}{10}\)
\(\Rightarrow\frac{x}{x+1}=\frac{9}{10}\)
\(\Rightarrow x=9\)
DD
Đoàn Đức Hà
Giáo viên
10 tháng 1 2021
b) \(\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{13.15}+x=\frac{1}{3}\)
\(\Leftrightarrow\frac{5-3}{3.5}+\frac{7-5}{5.7}+...+\frac{15-13}{13.15}+x=\frac{1}{3}\)
\(\Leftrightarrow\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{13}-\frac{1}{15}+x=\frac{1}{3}\)
\(\Leftrightarrow\frac{1}{3}-\frac{1}{15}+x=\frac{1}{3}\)
\(\Leftrightarrow x=\frac{1}{15}\)
NT
0
UN
2
BD
6 tháng 7 2023
\(x-\left(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}\right)=1\)
\(x-\left(\dfrac{1}{1\times2}+\dfrac{1}{2\times3}+\dfrac{1}{3\times4}+\dfrac{1}{5\times4}+\dfrac{1}{5\times6}+\dfrac{1}{7\times6}\right)=1\)
\(x-\left(1-\dfrac{1}{2}+\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}\right)=1\)
\(x-\left(1-\dfrac{1}{7}\right)=1\)
\(x-1+\dfrac{1}{7}=1\)
\(x+\dfrac{1}{7}=1+1\)
\(x+\dfrac{1}{7}=2\)
\(x=2-\dfrac{1}{7}\)
\(x=\dfrac{14-1}{7}=\dfrac{13}{7}\)
6 tháng 7 2023
Nguyễn Ngọc Ánh: nhầm dấu hơi nhìu nhưng c.ơn đã giải cho mik.
\(\frac{1}{x}+\frac{1}{2.x}+\frac{1}{6x}+\frac{1}{12x}+\frac{1}{30x}\)
= \(\frac{1}{x}\left(1+\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{30}\right)\)
= \(\frac{1}{x}\left(1+\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}\right)\)
= \(\frac{1}{x}\left(1+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\right)\)
=\(\frac{1}{x}\left(1+1-\frac{1}{6}\right)\)
=\(\frac{1}{x}.\frac{11}{6}\)
=\(\frac{11}{6x}\)