Question

tính
a=1/2.1+2/2.3+2/3.4+……+2/9.10
làm nhanh nha ít nhất là 12 giờ 30 nha

nhanh và đúng mk tick cho

Answer 1

\(A=\dfrac{1}{2.1}+\dfrac{2}{2.3}+\dfrac{2}{3.4}+...+\dfrac{2}{9.10}\)

\(=\dfrac{1}{2}+2\left(\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{9.10}\right)\)

\(=\dfrac{1}{2}+2\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{9}-\dfrac{1}{10}\right)\)

\(=\dfrac{1}{2}+2\left(\dfrac{1}{2}-\dfrac{1}{10}\right)\)

\(=\dfrac{1}{2}+1-\dfrac{1}{5}\)

\(=\dfrac{1}{2}+\dfrac{4}{5}=\dfrac{13}{10}\)

Vậy \(A=\dfrac{13}{10}\)