Question

\(1-\frac{2}{3\cdot5}-\frac{2}{5\cdot7}-\frac{2}{7\cdot9}-...-\frac{2}{61\cdot63}-\frac{2}{63\cdot65}\)

Answer 1

\(1-\frac{2}{3.5}-\frac{2}{5.7}-\frac{2}{7.9}-.......-\frac{2}{61.63}-\frac{2}{63.65}\)

=\(-1.\left(\frac{2}{3.5}+\frac{2}{5.7}+......\frac{2}{63.65}\right)+1\)

=\(-1.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+.......+\frac{1}{63}-\frac{1}{65}\right)+1\)

=\(-1.\left(\frac{1}{3}-\frac{1}{65}\right)+1\)

=\(-1.\frac{62}{195}+1\)

=\(\frac{-62}{195}+\frac{195}{195}\)

=\(\frac{133}{195}\)

Hok tốt nhé bn