Ta có;\(\frac{4}{1\times3}+\frac{4}{3\times5}+\frac{4}{5\times7}+....+\frac{4}{19\times21}\)
\(=2\times\left(\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+....+\frac{2}{19\times21}\right)\)
\(=2\times\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{19}-\frac{1}{21}\right)\)
\(=2\times\left(1-\frac{1}{21}\right)=2\times\frac{20}{21}=\frac{40}{21}\)
4/1 x 3 + 4/ 3 x 5 + 4/ 5 x 7 + ....+ 4/ 17 x 19 + 4/ 19 x 21
= 2 x ( 2/ 1 x 3 + 2/ 3 x 5 + 2/ 5 x 7 + ...+ 2/ 17 x 19 + 2/ 19 x 21 )
= 2 x ( 1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + ...+ 1/17 - 1/19 + 1/19 - 1/21 )
= 2 x ( 1 - 1/21 )
= 2 x 20/21
= 40/21
Chúc bạn học giỏi !!!
Đặt \(K=\frac{4}{1.3}+\frac{4}{3.5}+\frac{4}{5.7}+\frac{4}{7.9}+...+\frac{4}{17.19}+\frac{4}{19.21}\)
\(\Leftrightarrow K=\left(\frac{4}{1}-\frac{4}{3}\right)+\left(\frac{4}{3}-\frac{4}{5}\right)+\left(\frac{4}{5}-\frac{4}{7}\right)+\left(\frac{4}{7}-\frac{4}{9}\right)+...+\left(\frac{4}{19}-\frac{4}{21}\right)\)
\(\Leftrightarrow K=\frac{4}{1}-\frac{4}{3}+\frac{4}{3}-\frac{4}{5}+\frac{4}{5}-\frac{4}{7}+\frac{4}{7}-\frac{4}{9}+...+\frac{4}{19}-\frac{4}{21}\)
\(\Leftrightarrow K=\frac{4}{1}-\frac{4}{21}=\frac{84}{21}-\frac{4}{21}=\frac{80}{21}\)
Bạn TTH sai , bạn Hoàng Trung Kiên và mình đúng .
Lí do : 4/1 x 3 = 4/1 - 4/3 ???
Sai nhé !!!!