Tính nhanh: \(\Large B =\dfrac{4}{3\times6}+\dfrac{4}{6\times9}+\dfrac

Tính nhanh:

$\Large B =\dfrac{4}{3\times6}+\dfrac{4}{6\times9}+\dfrac{4}{9\times12}+\dfrac{4}{12\times15}$

(Điền kết quả dưới dạng phân số tối giản a/b)

• A. B = 16/45

Ta có : $\Large \dfrac{4}{3\times6}=\dfrac{4}{3} \times \dfrac{3}{3 \times 6} = \dfrac{4}{3} \times (\dfrac{1}{3} - \dfrac{1}{6})$

$\Large B =\dfrac{4}{3\times6}+\dfrac{4}{6\times9}+\dfrac{4}{9\times12}+\dfrac{4}{12\times15}$

$\Large B =\dfrac{4}{3}\times(\dfrac{1}{3}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{12}+\dfrac{1}{12}-\dfrac{1}{15})$

$\Large B =\dfrac{4}{3}\times(\dfrac{1}{3}-\dfrac{1}{15})$

$\Large B =\dfrac{4}{3}\times\dfrac{4}{15}$

$\Large B =\dfrac{16}{45}$