Question

[Nguyễn Lê Minh Quân]

tính bằng cách thuận tiện

A=1/3+1/6+1/10+...+1/45

Answer 1

[Nguyễn Thị Thương Hoài]

A = \(\dfrac{1}{3}\) + \(\dfrac{1}{6}\) + \(\dfrac{1}{10}\) + ... + \(\dfrac{1}{45}\)

A = \(\dfrac{2}{2}\) x (\(\dfrac{1}{3}\) + \(\dfrac{1}{6}\) + \(\dfrac{1}{10}\)+ ... + \(\dfrac{1}{45}\))

A = 2 x (\(\dfrac{1}{6}\) + \(\dfrac{1}{12}\)+ \(\dfrac{1}{20}\) + ... + \(\dfrac{1}{90}\))

A = 2 x (\(\dfrac{1}{2\times3}\) + \(\dfrac{1}{3\times4}\)+ ... + \(\dfrac{1}{9\times10}\))

A = 2 x (\(\dfrac{1}{2}\) - \(\dfrac{1}{3}\) + \(\dfrac{1}{3}\) - \(\dfrac{1}{4}\) + ... + \(\dfrac{1}{9}\) - \(\dfrac{1}{10}\))

A = 2 x (\(\dfrac{1}{2}\) - \(\dfrac{1}{10}\))

A = 2 x \(\dfrac{2}{5}\) 

A = \(\dfrac{1}{5}\)