Question

Tính tích A=(\(\frac{7}{9}\)+1)(\(\frac{7}{20}\)+1)(\(\frac{7}{33}\)+1)...(\(\frac{7}{2900}\)+1)

Answer 1

 \(A=\left(\frac{7}{9}+1\right)\left(\frac{7}{20}+1\right)\left(\frac{7}{33}+1\right)..........\left(\frac{7}{2900}+1\right)\)

 \(A=\frac{16}{9}.\frac{27}{20}.\frac{40}{33}.......\frac{2907}{2900}\)

 \(A=\frac{2.8}{1.9}.\frac{3.9}{2.10}.\frac{4.10}{3.11}......\frac{51.57}{50.58}\)

 \(A=\frac{2.3.4.....51}{1.2.3......50}.\frac{8.9.10.......57}{9.10.11........58}\)

 \(A=51.\frac{4}{29}\)

 \(A=\frac{204}{59}\)

Vậy \(A=\frac{204}{59}\)