Question

Tính nhanh

\(\frac{1}{3\times5}+\frac{1}{5\times7}\)\(+...+\frac{1}{19\times21}\)

Answer 1

=\(2\)x(\(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+....+\frac{1}{19}-\frac{1}{21}\))

=2x(\(\frac{1}{3}-\frac{1}{21}\))

=2x\(\frac{2}{7}\)

=\(\frac{4}{7}\)

Answer 2

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

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

\(2A=\frac{2}{3}-\frac{2}{5}+\frac{2}{5}-\frac{2}{7}+...+\frac{2}{19}-\frac{2}{21}\)

\(2A=\frac{2}{3}-\frac{2}{21}\)

\(2A=\frac{4}{7}\)

\(A=\frac{2}{7}\)

Answer 3

Mình sửa lại nha:

=\(\frac{1}{2}x\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+....+\frac{1}{19}-\frac{1}{21}\right)\)

=\(\frac{1}{2}x\left(\frac{1}{3}-\frac{1}{21}\right)\)

=\(\frac{1}{2}\)x\(\frac{2}{7}\)

=\(\frac{1}{7}\)