Question

A= (1 - 1/36 )( 1 - 1/45 )(1 - 1/55)...(1 - 1/300) = ?

Answer 1

\(A=\left(1-\frac{1}{36}\right)\left(1-\frac{1}{45}\right)\left(1-\frac{1}{55}\right)...\left(1-\frac{1}{300}\right)\)

=\(\frac{35}{36}.\frac{44}{45}.\frac{54}{55}...\frac{299}{300}\)

tiếp tục

Answer 2

\(A=\frac{35}{36}.\frac{44}{45}.\frac{54}{55}....\frac{299}{300}=\frac{70}{72}.\frac{88}{90}.\frac{108}{110}....\frac{598}{600}=\frac{7.10}{8.9}.\frac{8.11}{9.10}.\frac{9.12}{10.11}....\frac{23.26}{24.25}\)

\(A=\frac{\left(7.8.9...23\right).\left(10.11.12...26\right)}{\left(8.9.10...24\right).\left(9.10.11...25\right)}=\frac{7.26}{24.9}=\frac{182}{216}=\frac{91}{108}\)