Question

giúp mình với thanks

```
\frac{1}{5.9} \quad \frac{1}{9.13} \quad \frac{1}{13.17} \quad \frac{1}{17.21}
```

Answer 1

\(\dfrac{1}{5\cdot9}+\dfrac{1}{9\cdot13}+\dfrac{1}{13\cdot17}+\dfrac{1}{17\cdot21}\\ =\dfrac{1}{4}\cdot\left(\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{17}+\dfrac{1}{17}-\dfrac{1}{21}\right)\\ =\dfrac{1}{4}\cdot\left(\dfrac{1}{5}-\dfrac{1}{21}\right)\\ =\dfrac{1}{4}\cdot\dfrac{16}{105}=\dfrac{4}{105}\)