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\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}\)
\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}\)
\(=1-\frac{1}{5}\)
\(=\frac{4}{5}\)
\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{9900}\)
\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{98.99}+\frac{1}{99.100}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+....+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}+\frac{1}{100}\)
\(=1-\frac{1}{100}\)
\(=\frac{99}{100}\)
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( 1 + 1/2 + 1/6 ) : ( 1/6 + 1/12 + 1/20 )
= ( 1 + 2/3 ) : ( 1/4 + 1/20 )
= 5/3 : 3/10
= 5/3 x 10/3
= 50/9
\(\left(1+\frac{1}{2}+\frac{1}{6}\right):\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}\right)\)
=\(\frac{5}{3}:\frac{3}{10}\)
=\(\frac{50}{9}\)
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\(S=\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}\)
\(=\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}\)
\(=1-\dfrac{1}{6}=\dfrac{5}{6}\)
\(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}\)
\(=\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+\dfrac{1}{4\cdot5}+\dfrac{1}{5\cdot6}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}\)
\(=1-\dfrac{1}{6}=\dfrac{5}{6}\)
#Ayumu
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(1/2+1/6+1/12+1/20+...+1/72) : X = 3/4
(1/1x2+1/2x3+1/3x4+1/4x5+...+1/7x8) : X = 3/4
(1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/7-1/8) : X = 3/4
(1/1-1/8) : X = 3/4
7/8 : X = 3/4
X = 7/8 : 3/4
X = 7/6
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\(\frac{4}{5}\times\left(20-x\right)=4\)
\(20-x=4:\frac{4}{5}\)
\(20-x=5\) Mình Chúc Các Bn Học Giỏi !!!!!!!!!!!!!!!!!!!
\(x=20-5\)
\(x=15\)
(1/2+1/6+1/12+1/20) x (20 - x) =4
4/5 x (20-x)= 4
20-x=4:4/5
20-x=5
x=15
\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+........+\frac{1}{56}\)
\(=\frac{1}{1.2}+\frac{1}{2.3}+...........+\frac{1}{7.8}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+......+\frac{1}{7}-\frac{1}{8}\)
\(=1-\frac{1}{8}=\frac{7}{8}\)