tính giúp mình: 1/1*2+1/2*3+1/3*4+1/4*5 tính nhanh nha. 17/09/2021 Bởi Piper tính giúp mình: 1/1*2+1/2*3+1/3*4+1/4*5 tính nhanh nha.
`1/(1×2)+1/(2×3)+1/(3×4)+1/(4×5)` `=(2-1)/(1×2)+(3-2)/(2×3)+(4-3)/(3×4)+(5-4)/(4×5)` `=2/(1×2)-1/(1×2)+3/(2×3)-2/(2×3)+4/(3×4)-3/(3×4)+5/(4×5)-4/(4×5)` `=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5` `=1-1/5` `=4/5`. Bình luận
$\dfrac{1}{1 \times 2} +\dfrac{1}{2 \times 3} + \dfrac{1}{3 \times 4} + \dfrac{1}{4 \times 5}$ $= \dfrac{1}{1} – \dfrac{1}{2} + \dfrac{1}{2} – \dfrac{1}{3} + \dfrac{1}{3} – \dfrac{1}{4} + \dfrac{1}{4} – \dfrac{1}{5}$ $= 1 – \dfrac{1}{5}$ $= \dfrac{5}{5} – \dfrac{1}{5}$ $= \dfrac{4}{5}$. Bình luận
`1/(1×2)+1/(2×3)+1/(3×4)+1/(4×5)`
`=(2-1)/(1×2)+(3-2)/(2×3)+(4-3)/(3×4)+(5-4)/(4×5)`
`=2/(1×2)-1/(1×2)+3/(2×3)-2/(2×3)+4/(3×4)-3/(3×4)+5/(4×5)-4/(4×5)`
`=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5`
`=1-1/5`
`=4/5`.
$\dfrac{1}{1 \times 2} +\dfrac{1}{2 \times 3} + \dfrac{1}{3 \times 4} + \dfrac{1}{4 \times 5}$
$= \dfrac{1}{1} – \dfrac{1}{2} + \dfrac{1}{2} – \dfrac{1}{3} + \dfrac{1}{3} – \dfrac{1}{4} + \dfrac{1}{4} – \dfrac{1}{5}$
$= 1 – \dfrac{1}{5}$
$= \dfrac{5}{5} – \dfrac{1}{5}$
$= \dfrac{4}{5}$.