Question

tính nhanh:

B=\(\dfrac{1}{18}\)+\(\dfrac{1}{54}\)+\(\dfrac{1}{108}\)+....+\(\dfrac{1}{990}\)

Answer 1

`B=1/18 + 1/54 + 1/108 + ... + 1/990`

`= 1/(3xx6) + 1/(6xx9) + 1/(9xx12) + ...... + 1/(30xx33)`

`= 1/3 xx (1/3 - 1/6 + 1/6 - 1/9 + 1/9 - 1/12 + ...... + 1/30 - 1/33)`

`= 1/3 xx (1/3 - 1/33)`

`= 1/3 xx 10/33`

`= 10/99`

Answer 2

\(B=\dfrac{1}{18}+\dfrac{1}{54}+\dfrac{1}{108}+...+\dfrac{1}{990}\\ =\dfrac{1}{3.6}+\dfrac{1}{6.9}+\dfrac{1}{9.12}+...+\dfrac{1}{30.33}\\=\dfrac{1}{3}\left( \dfrac{3}{3.6}+\dfrac{3}{6.9}+\dfrac{3}{9.12}+...+\dfrac{3}{30.33}\right)\\ =\dfrac{1}{3}\left(\dfrac{1}{3}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{12}+...+\dfrac{1}{30}-\dfrac{1}{33}\right)\\ =\dfrac{1}{3}\left(\dfrac{1}{3}-\dfrac{1}{33}\right)\\ =\dfrac{1}{3}.\dfrac{10}{33}\\ =\dfrac{10}{99}\)