Question

[0o0 Ngốk 0o0]

Rút gọn

 \(A=\frac{10.11+50.55+70.77}{11.12+55.60+77.84}\)

\(B=\frac{1\times3\times5\times7\times.......\times49}{26\times27\times28\times............\times50}\)

\(C=\frac{1.2.6+2.4.12+4.8.12+4.8.24+7.14.42}{1.6.9+2.12.18+4.24.36+7.42.63}\)

Answer 1

[Hoàng Thị Thanh Huyền]

\(A=\frac{10.11+50.55+70.77}{11.12+55.60+77.84}\)

\(=\frac{10.11+5.10.5.11+7.10.7.11}{11.12+11.5.12.5+11.7.12.7}\)

\(=\frac{10.11\left(1+25+49\right)}{11.12\left(1+25+49\right)}\)

\(=\frac{10.11}{11.12}=\frac{10}{12}=\frac{5}{6}\)

\(B=\frac{1\times3\times5\times7\times........\times49}{26\times27\times28\times...........\times50}\)

\(=\frac{\left(1\times3\times5\times7\times.........\times49\right).\left(2\times4\times6.........48\times50\right)}{\left(26\times27\times28\times.........\times50\right).\left(2\times4\times6\times...........\times48\times50\right)}\)

\(=\frac{1\times2\times3\times4\times..........\times50}{\left(26\times27\times28\times..............\times50\right)2^{25}\left(1\times2\times3\times4\times............\times25\right)}=\frac{1}{2^{25}}\)

\(C=\frac{1.2.6+2.4.12+4.8.24+7.14.42}{1.6.9+2.12.18+4.24.36+7.42.63}\)

\(=\frac{1.2.6\left(1+8+64+343\right)}{1.6.9\left(1+8+64+343\right)}\)

\(=\frac{1.2.6}{1.6.9}=\frac{2}{9}\)

Answer 2

[Nguyễn Đình Toàn]

\(A=\frac{5}{6}\)

\(B=\frac{1}{33554432}\)

\(C=\frac{28}{117}\)