Question

\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+......+\frac{1}{19.21}\)

Answer 1

Đặt tên bthuc là A

\(A=\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{19.21}\)

\(2A=\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{19.21}\)

\(2A=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{19}-\frac{1}{21}\)

\(2A=1-\frac{1}{21}=\frac{20}{21}\)

=>\(A=\frac{20}{21}:2=\frac{10}{21}\)

Answer 2

\(=\frac{1}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{17.19}\right)\)

\(=\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{17}-\frac{1}{19}\right)\)

\(=\frac{1}{2}\left(1-\frac{1}{19}\right)=\frac{1}{2}.\left(\frac{18}{19}\right)\)

\(=\frac{9}{19}\)

Answer 3

sr nhìn nhầm đề bài

Answer 4

\(A=\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{19.21}\)

=>\(2A=\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{19.21}\)

=>\(2A=\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{19}-\frac{1}{21}\)

=>\(2A=1-\frac{1}{21}\)

=>\(2A=\frac{20}{21}\)

=>\(A=\frac{10}{21}\)

Answer 5

=1-1/3+1/3-1/5+1/5-1/7....+1/19-1/21

=1-1/21

=20/21

Answer 6

Đặt \(A=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{19.21}\)

          <=>\(2A=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{19.21}\)

          <=>\(2A=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{19}-\frac{1}{21}\)

          <=>\(2A=1-\frac{1}{21}\)

          <=>\(2A=\frac{20}{21}\)

          <=> \(A=\frac{10}{21}\)

Answer 7

thank các bạn nha