[tex]\text{Forma generala:}\boxed{\dfrac{1}{n(n+1)}=\dfrac{1}{n}-\dfrac{1}{n+1}}\\
a)\dfrac{1}{1\cdot 2}+\dfrac{1}{2\cdot 3}+_{\dots}+\dfrac{1}{29\cdot 30}=\\
=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+_{\dots}+\dfrac{1}{29}-\dfrac{1}{30}=\\
=1-\dfrac{1}{30}=\boxed{\dfrac{29}{30}}[/tex]
