Question

Tính:

A= \(\frac{3^2}{5.14}\)+\(\frac{3^2}{7.18}\)+\(\frac{3^2}{9.22}\)+\(\frac{3^2}{11.26}\)+\(\frac{3^2}{13.30}\).

Answer 1

A =\(\frac{3^2}{5.14}+\frac{3^2}{7.18}+\frac{3^2}{9.22}+\frac{3^2}{11.26}+\frac{3^2}{13.30}\)

A =\(3^2.\left(\frac{1}{5.14}+\frac{1}{7.18}+\frac{1}{9.22}+\frac{1}{11.26}+\frac{1}{13.30}\right)\)

A =\(9.\frac{1}{2}.\left(\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}+\frac{2}{13.15}\right)\)

A =\(\frac{9}{4}.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}\right)\)

A =\(\frac{9}{4}.\left(\frac{1}{5}-\frac{1}{15}\right)\)

A =\(\frac{9}{4}.\frac{2}{15}\)

A =\(\frac{3}{10}\)