Question

Giúp mình nhé. Mình cảm ơn rất nhiều

3/1*3+3/2*7+3/5*7+3/7*9+3/9*11

Answer 1

Ta có : \(\frac{3}{1.3}+\frac{3}{3.5}+\frac{3}{5.7}+.....+\frac{3}{9.11}\)

\(=\frac{3}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+.....+\frac{2}{9.11}\right)\)

\(=\frac{3}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+.....+\frac{1}{9}-\frac{1}{11}\right)\)

\(=\frac{3}{2}\left(1-\frac{1}{11}\right)=\frac{3}{2}.\frac{10}{11}=\frac{15}{11}\)

Answer 2

Ta có :

\(\frac{3}{1.3}+\frac{3}{3.5}+........+\frac{3}{9.11}\)

\(=\frac{3}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+.....+\frac{3}{9.11}\right)\)

\(=\frac{3}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+....+\frac{1}{9}-\frac{1}{11}\right)\)

\(=\frac{3}{2}\left(1-\frac{1}{11}\right)\)

\(=\frac{3}{2}.\frac{10}{11}=\frac{30}{22}\)