A = 1 + $\frac{1}{8}$ + $\frac{1}{24}$ + $\frac{1}{48}$ + $\frac{1}{80}$ + $\frac{1}{120}$
B = $\frac{2}{1.3}$ + $\frac{2}{3.5}$ + $\frac{2}{5.7}$ + … + $\frac{2}{97.99}$
A = 1 + $\frac{1}{8}$ + $\frac{1}{24}$ + $\frac{1}{48}$ + $\frac{1}{80}$ + $\frac{1}{120}$
B = $\frac{2}{1.3}$ + $\frac{2}{3.5}$ + $\frac{2}{5.7}$ + … + $\frac{2}{97.99}$
Đáp án+Giải thích các bước giải:
$\\A=1+\dfrac{1}{8}+\dfrac{1}{24}+\dfrac{1}{48}+\dfrac{1}{80}+\dfrac{1}{120}\\=1+\left[\dfrac{1}{2}.\left(\dfrac{2}{2.4}+\dfrac{2}{4.6}+\dfrac{2}{6.8}+\dfrac{2}{8.10}+\dfrac{1}{10.12}\right)\right]\\=1+\left[\dfrac{1}{2}.\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+…+\dfrac{1}{10}-\dfrac{1}{12}\right)\right]\\=1+\left[\dfrac{1}{2}.\left(\dfrac{1}{2}-\dfrac{1}{12}\right)\right]\\=1+\dfrac{5}{24}\\=\dfrac{29}{24}$
$\\B=\dfrac{2}{1.3}+\dfrac{2}{3.5}+…+\dfrac{2}{97.99}\\=1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+…+\dfrac{1}{97}-\dfrac{1}{99}\\=1-\dfrac{1}{99}=\dfrac{98}{99}$
$\text{Đáp án + Giải thích các bước giải:}$
`A=1+(1)/(8)+(1)/(24)+(1)/(48)+(1)/(80)+(1)/(120)`
`=>2A=2+(2)/(2.4)+(2)/(4.6)+(2)/(6.8)+(2)/(8.10)+(2)/(10.12)`
`=>2A=2+(1)/(2)-(1)/(4)+(1)/(4)-(1)/(6)+(1)/(6)-(1)/(8)+(1)/(8)-(1)/(10)+(1)/(10)-(1)/(12)`
`=>2A=2+(1)/(2)-(1)/(12)`
`=>A=1+(1)/(4)-(1)/(24)`
`=>A=(29)/(24)`
`————`
`B=(2)/(1.3)+(2)/(3.5)+(2)/(5.7)+…+(2)/(97.99)`
`=>B=1-(1)/(3)+(1)/(3)-(1)/(5)+(1)/(5)-(1)/(7)+….+(1)/(97)-(1)/(99)`
`=>B=1-(1)/(99)`
`=>B=(98)/(99)`