Tính giá trị biểu thức sau
(1+1/2).(1+1/3).(1+1/4).(1+1/5)
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\(\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+...+\frac{1}{9\times10}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{10}\)
\(=\frac{1}{2}-\frac{1}{10}=\frac{2}{5}\)
A=\(x.\dfrac{1}{5}+x.\dfrac{2}{3}-x.\dfrac{1}{4}\)
=\(x.\left(\dfrac{1}{5}+\dfrac{2}{3}-\dfrac{1}{4}\right)\)
=\(x.\dfrac{37}{60}\)
Thay x=\(\dfrac{1}{2}\) vào A ta được
A=\(\dfrac{1}{2}.\dfrac{37}{60}=\dfrac{37}{120}\)
`@` `\text {Ans}`
`\downarrow`
`(1/2-1/3+1/4-1/5):(1/4-1/5)`
`=`\(\left(\dfrac{1}{6}+\dfrac{1}{20}\right)\div\dfrac{1}{20}\)
`=`\(\dfrac{1}{20}\div\dfrac{1}{20}+\dfrac{1}{6}\div\dfrac{1}{20}\)
`= 1+10/3`
`= 13/3`
A = (\(\dfrac{1}{2}\) - \(\dfrac{1}{3}\) + \(\dfrac{1}{4}\) - \(\dfrac{1}{5}\)): (\(\dfrac{1}{4}\) - \(\dfrac{1}{5}\))
A = ( \(\dfrac{30}{60}\) - \(\dfrac{20}{60}\) + \(\dfrac{15}{60}\) - \(\dfrac{12}{60}\)):(\(\dfrac{5}{20}\) - \(\dfrac{4}{20}\))
A = \(\dfrac{13}{60}\): \(\dfrac{1}{20}\)
A = \(\dfrac{13}{60}\times\dfrac{20}{1}\)
A = \(\dfrac{13}{3}\)
(1+1/2).(1+1/3).(1+1/4).(1+1/5)
=3/2.4/3.5/4.6/5
=3.4.5.6/2.3.4.5
=6/2
=3
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