Tính $\frac{3}{2.3}$ + $\frac{3}{3.4}$ + $\frac{3}{4.5}$ +…+$\frac{3}{96.97}$ =

Tính $\frac{3}{2.3}$ + $\frac{3}{3.4}$ + $\frac{3}{4.5}$ +…+$\frac{3}{96.97}$ =

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  1. Đáp án:

     

    Giải thích các bước giải:

    \(S =\dfrac{3}{2.3}+\dfrac{3}{3.4}+\dfrac{3}{4.5}+…+\dfrac{3}{96.97}\)

    \(= 3.\left(\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+…+\dfrac{1}{96.97}\right)\)

    \(= 3.\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+…+\dfrac{1}{96}-\dfrac{1}{97}\right)\)

    \(= 3.\left(\dfrac{1}{2}-\dfrac{1}{97}\right)\)

    \(= 3.\dfrac{95}{194}\)

    \(=\dfrac{285}{194}\)

    Vậy \(S =\dfrac{285}{194}\)

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  2. $\begin{array}{l}\underline{\text{Đáp án:}}\\\dfrac{3}{2.3}+\dfrac{3}{3.4}+\dfrac{3}{4.5}+….+\dfrac{3}{96.97}=\dfrac{285}{194}\\\underline{\text{Giải thích các bước giải:}}\\\dfrac{3}{2.3}+\dfrac{3}{3.4}+\dfrac{3}{4.5}+….+\dfrac{3}{96.97}\\=3.(\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+…………\dfrac{1}{96.97})\\=3.(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+……+\dfrac{1}{96}-\dfrac{1}{97})\\=3.(\dfrac{1}{2}-\dfrac{1}{97})\\=3.\dfrac{95}{194}\\=\dfrac{285}{194}\\\underline{\text{CHÚC BẠN HỌC TỐT}}\\\end{array}$

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