Question

tính: Q=3/2^2. 8/3^2. 15/4^2. ... . 899/30^2

Answer 1

\(Q=\dfrac{3}{2^2}.\dfrac{8}{3^2}.\dfrac{15}{4^2}.......................\dfrac{899}{30^2}\)

\(\Leftrightarrow Q=\dfrac{1.3.2.4.3.5........29.31}{2.2.3.3......30.30}\)

\(\Leftrightarrow Q=\dfrac{\left(2.3.....29.30\right)\left(3.4.5....29.31\right)}{\left(2.3.4....30\right)\left(2.3.4....30\right)}\)

\(\Leftrightarrow Q=\dfrac{31}{2.30}\)

\(\Leftrightarrow Q=\dfrac{31}{60}\)

Answer 2

A=\(\dfrac{3}{2^2}\)x\(\dfrac{8}{3^2}\)x\(\dfrac{15}{4^2}\)......\(\dfrac{899}{30^2}\)=\(\dfrac{1.3.2.4.3.5....29.31}{2.2.3.3.4.4....30.30}\)= (\(\dfrac{2.3....29.30}{2.3....20.30}\)).(\(\dfrac{3.4.5....29.31}{2.3.4....29.30}\))=\(\dfrac{31}{2.30}\)=\(\dfrac{31}{60}\)