Lời giải:
\(A=\frac{1\times 5+4}{1\times 5}\times \frac{2\times 6+4}{2\times 6}\times \frac{3\times 7+4}{3\times 7}\times ....\times \frac{20\times 24+4}{20\times 24}\)
\(=\frac{9}{1\times 5}\times \frac{16}{2\times 6}\times \frac{25}{3\times 7}\times ....\times \frac{484}{20\times 24}\)
\(=\frac{9\times 16\times 25\times...\times 484}{(1\times 5)\times (2\times 6)\times (3\times 7)\times....\times (20\times 24)}\)
\(=\frac{3^2\times 4^2\times...\times 22^2}{(1\times 2\times 3\times...\times 20)\times (5\times 6\times ....\times 24)}\)
\(=\frac{(3\times 4\times ...\times 22)\times (3\times 4\times....\times 22)}{(1\times 2\times 3...\times 20)\times (5\times 6\times ....\times 24)}=\frac{21\times 22}{2}\times \frac{3\times 4}{23\times 24}=\frac{231}{46}\)
Ta có: \(A=\left(1+\dfrac{4}{1\cdot5}\right)\left(1+\dfrac{4}{2\cdot6}\right)\cdot\left(1+\dfrac{4}{3\cdot7}\right)\cdot...\cdot\left(1+\dfrac{4}{20\cdot24}\right)\)
\(=\left(1+1-\dfrac{1}{5}\right)\left(1+\dfrac{1}{2}-\dfrac{1}{6}\right)\left(1+\dfrac{1}{3}-\dfrac{1}{7}\right)\cdot...\cdot\left(1+\dfrac{1}{20}-\dfrac{1}{24}\right)\)
\(=\dfrac{3^2}{5}\cdot\dfrac{16}{2\cdot6}\cdot\dfrac{25}{3\cdot7}\cdot...\cdot\dfrac{484}{20\cdot24}\)
\(=\dfrac{231}{46}\)
Giải:
\(A=\left(1+\dfrac{4}{1.5}\right).\left(1+\dfrac{4}{2.6}\right).\left(1+\dfrac{4}{3.7}\right).....\left(1+\dfrac{4}{20.24}\right)\)
\(A=\dfrac{1.5+4}{1.5}.\dfrac{2.6+4}{2.6}.\dfrac{3.7+4}{3.7}.....\dfrac{20.24+4}{20.24}\)
\(A=\dfrac{9}{1.5}.\dfrac{16}{2.6}.\dfrac{25}{3.7}.....\dfrac{484}{20.24}\)
\(A=\dfrac{3^2.4^2.5^2.....22^2}{\left(1.5\right).\left(2.6\right).\left(3.7\right).....\left(20.24\right)}\)
\(A=\dfrac{3.3.4.4.5.5.....22.22}{\left(1.2.3.....20\right).\left(5.6.7.....24\right)}\)
\(A=\dfrac{\left(3.4.5.....22\right).\left(3.4.5.....22\right)}{\left(1.2.3.....20\right).\left(5.6.7.....24\right)}\)
\(A=\dfrac{21.22.3.4}{1.2.23.24}\)
\(A=\dfrac{231}{46}\)
Chúc bạn học tốt!
