Đáp án: Tính nhanh K=1/4+1/12+1/24+1/40+1/60+1/84+1/112 giải chi tiet cho minh nhe - Ta cóK = (1/2) ( (1/2) + (1/6) + (1/12) + (1/20) + (1/30) + (1/42) + (1/56) )= (1/2) ( (1/12) + (1/23) + (1/34) + (1/45) + (1/56) + (1/67) + (1/78) )= (1/2) ( 1 - (1/2) + (1/2) - (1/3) + (1/3) -(1/4) + (1/4) - (1/5) + (1/5) - (1/6) + (1/6) - (1/7) + (1/7) - (1/8) )= (1/2) ( 1 - (1/8) )= (1/2) (7/8)...

Ta cóK = (1/2) ( (1/2) + (1/6) + (1/12) + (1/20) + (1/30) + (1/42) + (1/56) )= (1/2) ( (1/12) + (1/23) + (1/34) + (1/45) + (1/56) + (1/67) + (1/78) )= (1/2) ( 1 - (1/2) + (1/2) - (1/3) + (1/3) -(1/4) + (1/4) - (1/5) + (1/5) - (1/6) + (1/6) - (1/7) + (1/7) - (1/8) )= (1/2) ( 1 - (1/8) )= (1/2) (7/8)...

Lê Na

2 năm trước

Tính nhanh K=1/4+1/12+1/24+1/40+1/60+1/84+1/112 giải chi tiet cho minh nhe

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namtran1997

2 năm trước

Ta có

$K = \dfrac{1}{2} \left( \dfrac{1}{2} + \dfrac{1}{6} + \dfrac{1}{12} + \dfrac{1}{20} + \dfrac{1}{30} + \dfrac{1}{42} + \dfrac{1}{56} \right)$

$= \dfrac{1}{2} \left( \dfrac{1}{1.2} + \dfrac{1}{2.3} + \dfrac{1}{3.4} + \dfrac{1}{4.5} + \dfrac{1}{5.6} + \dfrac{1}{6.7} + \dfrac{1}{7.8} \right)$

$= \dfrac{1}{2} \left( 1 - \dfrac{1}{2} + \dfrac{1}{2} - \dfrac{1}{3} + \dfrac{1}{3} -\dfrac{1}{4} + \dfrac{1}{4} - \dfrac{1}{5} + \dfrac{1}{5} - \dfrac{1}{6} + \dfrac{1}{6} - \dfrac{1}{7} + \dfrac{1}{7} - \dfrac{1}{8} \right)$

$= \dfrac{1}{2} \left( 1 - \dfrac{1}{8} \right)$

$= \dfrac{1}{2} . \dfrac{7}{8} = \dfrac{7}{16}$.