Ta có:\(\frac{1.3.5......39}{21.22.23........4}=\frac{1.3.5....39.2.4.6...40}{21.22.23......40.2.4.6.....40}\)

=\(\frac{40!}{21.22....40\left(1.2.3....20\right).2^{20}}\)

=\(\frac{40!}{40!2^{20}}=\frac{1}{2^{20}}\)

CM: \(\dfrac{1\cdot3\cdot5\cdot7\cdot\cdot\cdot39}{21\cdot22\cdot23\cdot\cdot\cdot40}=\dfrac{1}{2^{20}}\)

Biến đổi vế trái:

\(\dfrac{1\cdot3\cdot5\cdot7\cdot\cdot\cdot39}{21\cdot22\cdot23\cdot\cdot\cdot40}=\dfrac{1\cdot3\cdot5\cdot7\cdot\cdot\cdot19}{22\cdot24\cdot26\cdot\cdot\cdot40}\)

\(=\dfrac{1\cdot3\cdot5\cdot7\cdot\cdot\cdot19}{2\cdot11\cdot2^3\cdot3\cdot2\cdot13\cdot2^2\cdot7\cdot2\cdot15\cdot2^5\cdot2\cdot17\cdot2^2\cdot9\cdot2\cdot19\cdot2^3\cdot5}\)

\(=\dfrac{1\cdot3\cdot5\cdot7\cdot\cdot\cdot19}{\left(3\cdot5\cdot7\cdot\cdot\cdot19\right)2^{20}}\)

\(=\dfrac{1}{2^{20}}\)

bài này kêu mình làm gì vậy bạn

\(\frac{1\cdot3\cdot5\cdot......\cdot39}{21\cdot22\cdot23\cdot.....\cdot40}=\frac{(1\cdot3\cdot5\cdot....\cdot39)(2\cdot4\cdot6\cdot....\cdot40)}{(21\cdot22\cdot23\cdot....\cdot40)(2\cdot4\cdot6\cdot....\cdot40)}\)

\(=\frac{1\cdot2\cdot3\cdot....\cdot39\cdot40}{21\cdot22\cdot23\cdot....\cdot40\cdot(1\cdot2\cdot3\cdot....\cdot20)\cdot2^{10}}=\frac{1}{2^{10}}\)

P/S : Hoq chắc :>

\(\frac{1.3.5.7.9.....39}{21.22.23.24....40}\)

nhân cả tử và mẫu với 2,4,6,8,...,40 ta được:

\(\frac{\left(1.3.5.7.9.....39\right).\left(2.4.6.8.10.....40\right)}{\left(21.22.23....39.40\right).\left(2.4.6.8.10....40\right)}\)

\(=\frac{1..3.4.5.6.....39.40}{\left(21.22.23....40\right)\left(1.2.2.2.2.3.2.4...2.19.2.20\right)}\)

\(=\frac{1.2.3.4.5.6.7...39.40}{\left(1.2.3.4.5....39.40\right)2^{20}}\)

\(=\frac{1}{2^{20}}\)

Nhân cả tử và mẫu của phân số \(\frac{1.3.5...39}{21.22.23...40}\) ta được:

\(\frac{\left(1.3.5...39\right).\left(2.4.6...40\right)}{\left(21.22.23...40\right).\left(2.4.6...40\right)}=\frac{1.2.3...39.40}{21.22.23...40.\left[\left(1.2\right).\left(2.2\right)....\left(2.20\right)\right]}\)

\(=\frac{1.2.3...39.40}{21.22.23...40.\left(1.2.3...20\right).2^{30}}=\frac{1.2.3...39.40}{1.2.3...20.21....40.2^{20}}=\frac{1}{2^{20}}\)

Suy ra điều phải chứng minh.

Úi nhầm ở chỗ kia phải là 2²⁰

\(\frac{1.3.5.7...39}{21.22.23...40}=\frac{\left(2.4.6.8...40\right).\left(1.3.5.7...39\right)}{\left(2.4.6.8...40\right).\left(21.22.23...40\right)}=\frac{1.2.3.4...40}{^{2^{20}.1.2.3.4...40}}=\frac{1}{2^{20}}\)

\(\frac{1.3.5.7....39}{21.22.23....40}=\frac{\left(2.4.6....40\right).\left(1.3.5.7....39\right)}{\left(2.4.6....40\right).\left(21.22.23...40\right)}=\frac{1.2.3.4....40}{2^{20}.1.2.3.4....40}=\frac{1}{2^{20}}\)