Question

tính

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

Answer 1

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

= \(\dfrac{2}{2}+\dfrac{2}{6}+\dfrac{2}{12}+...+\dfrac{2}{90}\)

= \(\dfrac{2}{1.2}+\dfrac{2}{2.3}+\dfrac{2}{3.4}+...+\dfrac{2}{9.10}\)

= 2(\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{9.10}\))

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

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

= 2.\(\dfrac{9}{10}\)

= \(\dfrac{9}{5}\)

@Linh Xinh