Toán Tìm x biết (1/1×2×3×4+1/2×3×4×5+…+1/7×8×9×10)×x=119/720 06/07/2021 By Cora Tìm x biết (1/1×2×3×4+1/2×3×4×5+…+1/7×8×9×10)×x=119/720
Giải thích các bước giải: $(\dfrac{1}{1.2.3.4}+\dfrac{1}{2.3.4.5}+..+\dfrac{1}{7.8.9.10})x=\dfrac{119}{720}$ $\to (\dfrac{3}{1.2.3.4}+\dfrac{3}{2.3.4.5}+..+\dfrac{3}{7.8.9.10})x=\dfrac{119}{240}$ $\to (\dfrac{4-1}{1.2.3.4}+\dfrac{5-2}{2.3.4.5}+..+\dfrac{10-7}{7.8.9.10})x=\dfrac{119}{240}$ $\to (\dfrac{1}{1.2.3}-\dfrac{1}{2.3.4}+\dfrac{1}{2.3.4}-\dfrac{1}{3.4.5}+..+\dfrac{1}{7.8.9}-\dfrac{1}{8.9.10})x=\dfrac{119}{240}$ $\to (\dfrac{1}{1.2.3}-\dfrac{1}{8.9.10})x=\dfrac{119}{240}$ $\to \dfrac{119}{720}x=\dfrac{119}{240}$ $\to x=3$ Trả lời
Giải thích các bước giải:
$(\dfrac{1}{1.2.3.4}+\dfrac{1}{2.3.4.5}+..+\dfrac{1}{7.8.9.10})x=\dfrac{119}{720}$
$\to (\dfrac{3}{1.2.3.4}+\dfrac{3}{2.3.4.5}+..+\dfrac{3}{7.8.9.10})x=\dfrac{119}{240}$
$\to (\dfrac{4-1}{1.2.3.4}+\dfrac{5-2}{2.3.4.5}+..+\dfrac{10-7}{7.8.9.10})x=\dfrac{119}{240}$
$\to (\dfrac{1}{1.2.3}-\dfrac{1}{2.3.4}+\dfrac{1}{2.3.4}-\dfrac{1}{3.4.5}+..+\dfrac{1}{7.8.9}-\dfrac{1}{8.9.10})x=\dfrac{119}{240}$
$\to (\dfrac{1}{1.2.3}-\dfrac{1}{8.9.10})x=\dfrac{119}{240}$
$\to \dfrac{119}{720}x=\dfrac{119}{240}$
$\to x=3$