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