`14/13 + ( (-1)/3 - 19/20)`
`= 14/13 + (-1)/3 - 19/20`
`= 13/13 -19/20`
`= 1 -19/20`
`= 20/20 -19/20`
`=1/20`
` 14/13 + ( -1/13 - 19/20 ) `
`= (14/13 + (-1)/13) - 19/20 `
`= 1 - 19/20 `
`= 1/20`
P=\(\dfrac{20+\dfrac{19}{13}+\dfrac{19}{101}}{7+\dfrac{7}{13}+\dfrac{7}{19}+\dfrac{7}{101}}\)
CMR \(1-\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{5}-\dfrac{1}{6}+...+\dfrac{1}{19}-\dfrac{1}{20}=\dfrac{1}{11}+\dfrac{1}{12}+\dfrac{1}{13}+...+\dfrac{1}{20}\)
Tính:
\(\dfrac{7}{13}.\dfrac{5}{19}+\dfrac{7}{19}.\dfrac{8}{13}-3.\dfrac{7}{19}\)
Tìm x biết: \(\dfrac{13}{14}+\dfrac{13}{35}+\dfrac{13}{65}+\dfrac{13}{104}+...+\dfrac{13}{1274}-x+2\dfrac{1}{5}=0\)
CMR 1.3.5...19=\(\dfrac{11}{2}.\dfrac{12}{2}.\dfrac{13}{2}...\dfrac{20}{2}\)
\(Tìm\) \(x\)∈\(Z\)\(,\) \(biết\)\(:\)
\(a\)) \(\left(x-20\right)+\left(x-19\right)+\left(x-18\right)+...+99+100=100\)
\(b\)) \(213-x.\left(\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{2020}}\right):\left(1-\dfrac{1}{2^{2020}}\right)=13\)
Tính nhanh:
\(A=\dfrac{5}{13}=\dfrac{-5}{7}+\dfrac{-20}{41}+\dfrac{8}{13}+\dfrac{-21}{41}\)
Chứng tỏ rằng:
\(\dfrac{1}{5}+\dfrac{1}{13}+\dfrac{1}{14}+\dfrac{1}{15}+\dfrac{1}{61}+\dfrac{1}{62}+\dfrac{1}{63}< \dfrac{1}{2}\)
So sánh:
\(\dfrac{13}{19};\dfrac{47}{53}\)
