Question

Tinhs nhanh tổng sau:

A=1/3+1/6+1/10+1/15+...+1/120

Answer 1

A =  \(\dfrac{1}{3}\) + \(\dfrac{1}{6}\) + \(\dfrac{1}{10}\) +  \(\dfrac{1}{15}\) +.. .  + \(\dfrac{1}{120}\)

A =  \(\dfrac{2}{2}\).(\(\dfrac{1}{3}\) + \(\dfrac{1}{6}\) + \(\dfrac{1}{10}\) + \(\dfrac{1}{15}\) + ... + \(\dfrac{1}{120}\))

A = 2.( \(\dfrac{1}{6}\) + \(\dfrac{1}{12}\) + \(\dfrac{1}{20}\) + \(\dfrac{1}{30}\) + ... + \(\dfrac{1}{240}\))

A = 2.( \(\dfrac{1}{2.3}\) + \(\dfrac{1}{3.4}\) + \(\dfrac{1}{4.5}\) + \(\dfrac{1}{5.6}\) + ... + \(\dfrac{1}{15.16}\))

A  =2 .( \(\dfrac{1}{2}\) - \(\dfrac{1}{3}\) + \(\dfrac{1}{3}\) - \(\dfrac{1}{4}\) + \(\dfrac{1}{4}\) - \(\dfrac{1}{5}\) + \(\dfrac{1}{5}\) - \(\dfrac{1}{6}\) + \(\dfrac{1}{15}\) - \(\dfrac{1}{16}\))

A = 2.( \(\dfrac{1}{2}\) - \(\dfrac{1}{16}\))

A = 2.\(\dfrac{7}{16}\)

A = \(\dfrac{7}{8}\)