Tính giá trj biểu thức A= 3/1.4+ 3/4.7+ 3/7.10+3/10.13+ 3/13.16.

10/10

Tính ${\rm{A}} = \frac{3}{{1.4}} + \frac{3}{{4.7}} + \frac{3}{{7.10}} + \frac{3}{{10.13}} + \frac{3}{{13.16}}$.

$\frac{15}{61}$

$\frac{51}{16}$

$\frac{16}{15}$

$\frac{15}{16}$

Giải thích

Đáp án đúng là: D

${\rm{A}} = \frac{3}{{1.4}} + \frac{3}{{4.7}} + \frac{3}{{7.10}} + \frac{3}{{10.13}} + \frac{3}{{13.16}}$

$ = \frac{{4 - 1}}{{1.4}} + \frac{{7 - 4}}{{4.7}} + \frac{{10 - 7}}{{7.10}} + \frac{{13 - 10}}{{10.13}} + \frac{{16 - 13}}{{13.16}}$

$ = \frac{4}{{1.4}} - \frac{1}{{1.4}} + \frac{7}{{4.7}} - \frac{4}{{4.7}} + \frac{{10}}{{7.10}} - \frac{7}{{7.10}} + \frac{{13}}{{10.13}} - \frac{{10}}{{10.13}} + \frac{{16}}{{13.16}} - \frac{{13}}{{13.16}}$

$ = 1 - \frac{1}{4} + \frac{1}{4} - \frac{1}{7} + \frac{1}{7} - \frac{1}{{10}} + \frac{1}{{10}} - \frac{1}{{13}} + \frac{1}{{13}} - \frac{1}{{16}}$

$ = 1 - \frac{1}{{16}}$

$ = \frac{{15}}{{16}}$.