Question

\(\frac{3}{5\cdot7}+\frac{3}{7\cdot9}+........+\frac{3}{59\cdot61}\)

Answer 1

\(=\frac{3}{2}\left(\frac{2}{5.7}+\frac{2}{7.9}+.....+\frac{2}{59.61}\right)\)

\(=\frac{3}{2}\left(\frac{1}{5}-\frac{1}{61}\right)\)

\(=\frac{3}{2}.\frac{56}{305}\)

\(=\frac{84}{305}\)

tk cho minh nhe >.<

Answer 2

Ta có: \(\frac{2}{3}\times\left(\frac{3}{5.7}+\frac{3}{7.9}+.....+\frac{3}{59.61}\right):\frac{2}{3}\)

\(\Rightarrow\left(\frac{2}{5.7}+\frac{2}{7.9}+.....+\frac{2}{59.61}\right):\frac{2}{3}\)

\(=\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+....+\frac{1}{59}-\frac{1}{61}\right):\frac{2}{3}\)

\(\Rightarrow\left(\frac{1}{5}-\frac{1}{61}\right):\frac{2}{3}=\frac{56}{305}:\frac{2}{3}=\frac{84}{305}\)

Answer 3

= \(\frac{3}{2}\). ( \(\frac{2}{5.7}\)+ \(\frac{2}{7.9}\)+ ...... + \(\frac{2}{59.61}\))

= \(\frac{3}{2}\). ( \(\frac{1}{5}\)- \(\frac{1}{7}\)+ \(\frac{1}{7}\)- \(\frac{1}{9}\)+ ...... + \(\frac{1}{59}\)- \(\frac{1}{61}\))

= \(\frac{3}{2}\). ( \(\frac{1}{5}\)- \(\frac{1}{61}\))  = \(\frac{3}{2}\). \(\frac{61-5}{305}\)= \(\frac{3}{2}\). \(\frac{56}{305}\)

= \(\frac{3.28}{1.305}\)= \(\frac{82}{305}\)

Answer 4

A=3/5*7+3/7*9+...+3/59*61

2A=3(2/5*7+2/7*9+...+2/59*61)

2A=3*(1/5-1/7+1/7-1/9+1/9-1/11+...+1/59-1/61)

2A=3*(1/5-1/61)

2A=3*56/305

2A=168/305

A=84/305

nho k cho minh voi nhe

Answer 5

Đặt A=\(\frac{3}{5.7}+\frac{3}{7.9}+...+\frac{3}{59.61}\)

Ax\(\frac{2}{3}=\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{59.61}\)

Ax\(\frac{2}{3}=\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{59}-\frac{1}{61}\)

Ax\(\frac{2}{3}=\frac{1}{5}-\frac{1}{61}=\frac{56}{305}\)

A=\(\frac{56}{305}:\frac{2}{3}=\frac{84}{305}\)

Vậy A=\(\frac{84}{305}\)

Answer 6

=84/305