Simplify

​$$\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+\frac{1}{3\cdot4\cdot5}+\frac{1}{4\cdot5\cdot6}$$​​

Correct option is A

Given:

 $$\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+\frac{1}{3\cdot4\cdot5}+\frac{1}{4\cdot5\cdot6}$$​​

Solution:

$$\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+\frac{1}{3\cdot4\cdot5}+\frac{1}{4\cdot5\cdot6}$$​​

= $$\frac{1}{1\times2\times3}+\frac{1}{2\times3\times4}+\frac{1}{3\times4\times5}+\frac{1}{4\times5\times6}$$

= $$\frac{1}{6}+\frac{1}{24}+\frac{1}{60}+\frac{1}{120}$$

= $$\frac{20+5+2+1}{120}$$​

= $$\frac{28}{120}$$​

= $$\frac{7}{30}$$

Thus, the correct answer is (a).