\(S=\dfrac{3}{1.2}+\dfrac{3}{2.3}+...+\dfrac{3}{2015.2016}\)
\(=3\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{2015.2016}\right)\)
\(=3\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{2015}-\dfrac{1}{2016}\right)\)
\(=3\left(1-\dfrac{1}{2016}\right)\)
\(=3.\dfrac{2015}{2016}=\dfrac{6045}{2016}\)
Vậy \(S=\dfrac{6045}{2016}\)
\(S=3\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{2015.2016}\right)\)
\(\Rightarrow S=3\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{2015}-\dfrac{1}{2016}\right)\)
\(\Rightarrow S=3\left(1-\dfrac{1}{2016}\right)=3.\dfrac{2015}{2016}=\dfrac{6045}{2016}\)
Vậy ...
\(S=\dfrac{3}{1.2}+\dfrac{3}{2.3}+\dfrac{3}{3.4}+....+\dfrac{3}{2015.2016}\)
\(=\dfrac{1}{1}.\left(\dfrac{3}{1.2}+\dfrac{3}{2.3}+\dfrac{3}{3.4}+....+\dfrac{3}{2015.2016}\right)\)
= \(3.\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+....\dfrac{1}{2015.2016}\right)\)
= 3. \(\left(\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{2015}+\dfrac{1}{2016}\right)\)
= 3.
sorry em mình nghịch nên vẫn thiếu
bổ sung nè thêm vào chỗ " 3." nhé
= 3.\(\left(\dfrac{1}{1}-\dfrac{1}{2016}\right)\)
= 3.\(\dfrac{2015}{2016}\)
= \(\dfrac{6045}{2016}\)
Đúng thì tick nhé cả câu trả lời lúc nẫy ghép lại đấy, xin lỗi vì em tớ phá nên nó bị cách làm hai câu trả lời hưng thực ra là 1
\(S=\dfrac{3}{1.2}+\dfrac{3}{2.3}+\dfrac{3}{3.4}+...+\dfrac{3}{2015.2016}\)
\(3S=3.\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{2015.2016}\right)\)
\(3S=\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{2015}+\dfrac{1}{2016}\right)\)
\(3S=1-\dfrac{1}{2016}\)
\(S=3.\dfrac{2015}{2016}=\dfrac{6045}{2016}\)
Vậy.................................
)