Question

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

Answer 1

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

\(G=\dfrac{1.3}{2.2}.\dfrac{2.4}{3.3}.\dfrac{3.5}{4.4}....\dfrac{29.31}{30.30}\)

\(G=\dfrac{1.3.2.4.3.5....29.31}{2.2.3.3.4.4....30.30}\)

\(G=\dfrac{1.2.3....29}{2.3.4....30}.\dfrac{3.4.5....31}{2.3.4....30}\)

G=\(\dfrac{1}{30}.\dfrac{31}{2}=\dfrac{31}{60}\)

Answer 2

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

\(G=\dfrac{1.3}{2.2}.\dfrac{2.4}{3.3}.\dfrac{3.5}{4.4}................\dfrac{29.31}{30.30}\)

\(G=\dfrac{2.3.4...........30}{2.3.4.............30}.\dfrac{1.3.4..............31}{2.3.4.............30}\)

\(G=\dfrac{31}{2}\)