Question

Tính 1/1.3+1/3.5+1/3.7+.......+1/101.103

Answer 1

\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+....+\frac{1}{101.103}\)

=\(\frac{1}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+....+\frac{2}{101.103}\right)\)

=\(\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+....+\frac{1}{101}-\frac{1}{103}\right)\)

=\(\frac{1}{2}\left(1-\frac{1}{103}\right)\)

=\(\frac{1}{2}.\frac{102}{103}\)

=\(\frac{51}{103}\)

Answer 2

51/103