S=1/1×3+1/2×4+1/3×5+…+1/7×9+1/8×10

Đáp án:

Giải thích các bước giải:

 $S=\dfrac{1}{1.3}+\dfrac{1}{2.4}+\dfrac{1}{3.5}+…+\dfrac{1}{7.9}+\dfrac{1}{8.10}$

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$⇒2S=\dfrac{2}{1.3}+\dfrac{2}{2.4}+…+\dfrac{2}{7.9}+\dfrac{2}{8.10}$

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$=(\dfrac{2}{1.3}+\dfrac{2}{3.5}+…+\dfrac{2}{7.9})+(\dfrac{2}{2.4}+\dfrac{2}{4.6}+…+\dfrac{2}{8.10})$

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$=(1-\dfrac{1}{9})+(\dfrac{1}{2}-\dfrac{1}{10})$

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$=\dfrac{8}{9}+\dfrac{2}{5}$

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$=\dfrac{40}{45}+\dfrac{18}{45}$

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$=\dfrac{58}{45}$

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$⇒S=\dfrac{29}{45}$