Question

$D = 3 . 1/(1.2) - 5 . 1/(2.3) + 7. 1/(3.4) - .... + 15. 1/(7.8) - 17 . 1/(8.9)$

Answer 1

`D= 3/(1.2) - 5/(2.3) + 7/(3.4) - ... + 15/(7.8) - 17/(8.9)`

`D= (1+1/2) - (1/2 + 1/3) + (1/3- 1/4) -...+  (1/7+1/8)- (1/8+1/9)`

`D= 1-1/9`

`D= 8/9`

Vậy `D=8/9`

Answer 2

\(D=\dfrac{3}{1\cdot2}-\dfrac{5}{2\cdot3}+\dfrac{7}{3\cdot4}-...+\dfrac{15}{7\cdot8}-\dfrac{17}{8\cdot9}\)

\(=1+\dfrac{1}{2}-\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}+\dfrac{1}{4}-...+\dfrac{1}{7}+\dfrac{1}{8}-\dfrac{1}{8}-\dfrac{1}{9}\)

\(=1-\dfrac{1}{9}=\dfrac{8}{9}\)