Toán Tính nhanh K=1/4+1/12+1/24+1/40+1/60+1/84+1/112 giải chi tiet cho minh nhe 08/09/2021 By Emery Tính nhanh K=1/4+1/12+1/24+1/40+1/60+1/84+1/112 giải chi tiet cho minh nhe
Ta có $K = \dfrac{1}{2} \left( \dfrac{1}{2} + \dfrac{1}{6} + \dfrac{1}{12} + \dfrac{1}{20} + \dfrac{1}{30} + \dfrac{1}{42} + \dfrac{1}{56} \right)$ $= \dfrac{1}{2} \left( \dfrac{1}{1.2} + \dfrac{1}{2.3} + \dfrac{1}{3.4} + \dfrac{1}{4.5} + \dfrac{1}{5.6} + \dfrac{1}{6.7} + \dfrac{1}{7.8} \right)$ $= \dfrac{1}{2} \left( 1 – \dfrac{1}{2} + \dfrac{1}{2} – \dfrac{1}{3} + \dfrac{1}{3} -\dfrac{1}{4} + \dfrac{1}{4} – \dfrac{1}{5} + \dfrac{1}{5} – \dfrac{1}{6} + \dfrac{1}{6} – \dfrac{1}{7} + \dfrac{1}{7} – \dfrac{1}{8} \right)$ $= \dfrac{1}{2} \left( 1 – \dfrac{1}{8} \right)$ $= \dfrac{1}{2} . \dfrac{7}{8} = \dfrac{7}{16}$. Trả lời
Ta có
$K = \dfrac{1}{2} \left( \dfrac{1}{2} + \dfrac{1}{6} + \dfrac{1}{12} + \dfrac{1}{20} + \dfrac{1}{30} + \dfrac{1}{42} + \dfrac{1}{56} \right)$
$= \dfrac{1}{2} \left( \dfrac{1}{1.2} + \dfrac{1}{2.3} + \dfrac{1}{3.4} + \dfrac{1}{4.5} + \dfrac{1}{5.6} + \dfrac{1}{6.7} + \dfrac{1}{7.8} \right)$
$= \dfrac{1}{2} \left( 1 – \dfrac{1}{2} + \dfrac{1}{2} – \dfrac{1}{3} + \dfrac{1}{3} -\dfrac{1}{4} + \dfrac{1}{4} – \dfrac{1}{5} + \dfrac{1}{5} – \dfrac{1}{6} + \dfrac{1}{6} – \dfrac{1}{7} + \dfrac{1}{7} – \dfrac{1}{8} \right)$
$= \dfrac{1}{2} \left( 1 – \dfrac{1}{8} \right)$
$= \dfrac{1}{2} . \dfrac{7}{8} = \dfrac{7}{16}$.