\(D=\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+...+\dfrac{1}{19.20}\dfrac{ }{ }\dfrac{ }{ }\)
\(D=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{19}-\dfrac{1}{20}\)
\(D=\dfrac{1}{2}-\dfrac{1}{20}\)
\(D=\dfrac{10}{20}-\dfrac{1}{20}\)
\(D=\dfrac{9}{20}\)
\(----------------\)
\(E=\dfrac{1}{99}-\dfrac{1}{99.98}-\dfrac{1}{98.97}-...-\dfrac{1}{3.2}-\dfrac{1}{2.1}\)
\(E=\dfrac{1}{99}-\left(\dfrac{1}{99.98}+\dfrac{1}{98.97}+...+\dfrac{1}{3.2}+\dfrac{1}{2.1}\right)\)
\(E=\dfrac{1}{99}-\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{97.98}+\dfrac{1}{98.99}\right)\)
\(E=\dfrac{1}{99}-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{97}-\dfrac{1}{98}+\dfrac{1}{98}-\dfrac{1}{99}\right)\)
\(E=\dfrac{1}{99}-\left(1-\dfrac{1}{99}\right)\)
\(E=\dfrac{1}{99}-\left(\dfrac{99}{99}-\dfrac{1}{99}\right)\)
\(E=\dfrac{1}{99}-\dfrac{98}{99}\)
\(=\dfrac{-97}{99}\)
5A:
a, \(\dfrac{1}{3}x=\dfrac{5}{6}-\dfrac{1}{4}\)
\(\dfrac{1}{3}x=\dfrac{10}{12}-\dfrac{3}{12}\)
\(\dfrac{1}{3}x=\dfrac{7}{12}\)
\(x=\dfrac{7}{12}:\dfrac{1}{3}\)
\(x=\dfrac{7}{12}.3\)
\(x=\dfrac{7}{4}\)
Vậy \(x=\dfrac{7}{4}\)
\(b.\dfrac{1}{10}-\left(x-\dfrac{8}{25}\right)=\dfrac{1}{10}\)
\(x-\dfrac{8}{25}=\dfrac{1}{10}-\dfrac{1}{10}\)
\(x-\dfrac{8}{25}=0\)
\(x=0+\dfrac{8}{25}\)
\(x=\dfrac{8}{25}\)
Vậy \(x=\dfrac{8}{25}\)
( ý b tại mình nhìn ko rõ á mình chỉ thấy mấu số là 25 thui nên là có sai thì bn bảo mình nhé)
`D = 1/(2*3) + 1/(3*4) + 1/(4*5) + ... + 1/(19*20)`
`D = 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + ...+ 1/19 - 1/20`
`D = 1/2 - 1/20`
`D = 9/20`
`E = 1/99 - 1/(99*98) - 1/(98*97) - ... - 1/(3*2) - 1/(2*1)`
`E = 1/99 - (1/(99*98) + 1/(98*97) + ... + 1/(3*2) + 1/(2*1)`
`E = 1/99 - (1/99 - 1/98 + 1/98 - 1/97 + .... + 1/3 - 1/2 + 1/2 - 1`
`E = 1/99 - (1/99 - 1)`
`E = 1/99 - (1 - 1/99)`
E = 1/99 - 98/99`
E = -97/99`
`-----`
Tìm `x`
`a, 1/3 x = 5/6 - 1/4`
`=> 1/3 x = 10/12 - 3/12`
`=> 1/3 x = 7/12`
`=> x = 7/12 : 1/3`
`=> x = 7/4 `
Vậy `x = 7/4`
`b, 1/10 - (x - 8/25) = 1/10`
`=> x - 8/25 = 1/10 - 1/10`
`=> x - 8/25 = 0`
`=> x = 0 + 8/25`
`=> x = 8/25`
Vậy `x = 8/25`
