tính a=2^3 1)(3^3 1)...(100^3 1)/(2^3-1)(3^3-1)...(100^3-1)

483/726

Tính A=23+133+1...1003+123−133−1...1003−1

Nhập câu trả lời ở đây

0/3000 ký tự

Giải thích

Lời giải:

\(A = \frac{{\left( {{2^3} + 1} \right)\left( {{3^3} + 1} \right)...\left( {{{100}^3} + 1} \right)}}{{\left( {{2^3} - 1} \right)\left( {{3^3} - 1} \right)...\left( {{{100}^3} - 1} \right)}}\)

\(A = \frac{{\left( {2 + 1} \right)\left( {{2^2} - 2 + 1} \right)\left( {3 + 1} \right)\left( {{3^2} - 3 + 1} \right)...\left( {100 + 1} \right)\left( {{{100}^2} - 100 + 1} \right)}}{{\left( {2 - 1} \right)\left( {{2^2} + 2 + 1} \right)\left( {3 - 1} \right)\left( {{3^2} + 3 + 1} \right)...\left( {100 - 1} \right)\left( {{{100}^2} + 100 + 1} \right)}}\)

\(A = \frac{{3.3.4.7...101.9901}}{{1.7.2.13.3.21...99.10101}}\)

\(A = \frac{{\left( {3.4.5...101} \right).\left( {3.7.13...9901} \right)}}{{\left( {1.2.3...99} \right).\left( {7.13.21...10101} \right)}}\)

\(A = \frac{{3.100.101}}{{1.2.10101}} = \frac{{30300}}{{20202}}\)