Question

[Nguyen Danny]

3^2/4 + 3^2/18 + 3^2/54 + 3^2/108 + 3^2/180 + 3^2/270

Answer 1

[Nguyễn Thị Thương Hoài]

  A = \(\dfrac{3^2}{4}\) + \(\dfrac{3^2}{18}\) + \(\dfrac{3^2}{54}\) + \(\dfrac{3^2}{108}\) + \(\dfrac{3^2}{180}\) + \(\dfrac{3^2}{270}\)

A = \(\dfrac{9}{4}\) + \(\dfrac{1}{2}\) + \(\dfrac{1}{6}\) + \(\dfrac{1}{12}\) + \(\dfrac{1}{20}\) + \(\dfrac{1}{30}\)

A = \(\dfrac{9}{4}\)  + \(\dfrac{1}{1.2}\) + \(\dfrac{1}{2.3}\) + \(\dfrac{1}{3.4}\) + \(\dfrac{1}{4.5}\) + \(\dfrac{1}{5.6}\)

A = \(\dfrac{9}{4}\) + (\(\dfrac{1}{1}\) - \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) - \(\dfrac{1}{3}\) + \(\dfrac{1}{3}\) - \(\dfrac{1}{4}\) + \(\dfrac{1}{4}\) - \(\dfrac{1}{5}\) + \(\dfrac{1}{5}\) - \(\dfrac{1}{6}\))

A = \(\dfrac{9}{4}\) + \(\dfrac{1}{1}\) - \(\dfrac{1}{6}\)

A = \(\dfrac{54}{24}\) + \(\dfrac{24}{24}\) - \(\dfrac{4}{24}\)

A = \(\dfrac{78}{24}\) - \(\dfrac{4}{24}\)

A = \(\dfrac{37}{12}\)