F = 2/ 1*5 + 2/ 5*9 + …. + 2/ 81* 85 G= 3/ 4*9 + 3/ 9* 14 + 3/ 14* 19 + …. + 3/ 34* 39

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1. Đáp án:

    

   Giải thích các bước giải:

    F=2/4×(4/1×5+…..+4/81×85)

    F=1/2×(1-1/5+1/5-1/9+…..+1/81×1/85)

    F=1/2×(1-1/85)

    F=1/2×84/85

    F=42/85

   G=3/4×9+……+3/34×39

   G=3/5×(5/4×9+…..+5/34×39)

   G=3/5×(1/4-1/9+…+1/34-1/39)

   G=3/5×(1/4-1/39)

   G=3/5×35/156

   G=7/52

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2. 1)  F = $\frac{2}{1×5}$ + $\frac{2}{5×9}$ + … + $\frac{2}{81×85}$

        F = $\frac{1}{2}$ x ( $\frac{4}{1×5}$ + $\frac{4}{5×9}$ + … + $\frac{4}{81×85}$

        F = $\frac{1}{2}$ x ( 1 – $\frac{1}{5}$ + $\frac{1}{5}$ – $\frac{1}{9}$ + … + $\frac{1}{81}$ – $\frac{1}{85}$  ))

        F = $\frac{1}{2}$ x ( 1 – $\frac{1}{85}$ )

        F = $\frac{1}{2}$ x $\frac{84}{85}$

        F =  $\frac{42}{85}$

    Vậy F = $\frac{42}{85}$

   2)  G = $\frac{3}{4×9}$ + $\frac{3}{9×14}$+ …. + $\frac{3}{34×39}$

        G = $\frac{3}{5}$ x ( $\frac{5}{4×9}$ + $\frac{5}{9×14}$ + … + $\frac{5}{34×39}$

        G = $\frac{3}{5}$ x ( $\frac{1}{4}$ – $\frac{1}{9}$ + $\frac{1}{9}$ – $\frac{1}{14}$ + … + $\frac{1}{34}$ – $\frac{1}{39}$

        G = $\frac{3}{5}$ x ( $\frac{1}{4}$ – $\frac{1}{39}$ )

        G = $\frac{3}{5}$ x  $\frac{35}{156}$

        G = $\frac{7}{52}$

   Vậy G = $\frac{7}{52}$

    

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