Find the value of $\frac{1}{20} + \frac{1}{30} + \frac{1}{42} + \frac{1}{56} + \frac{1}{72} + \frac{1}{90}$ Find the value of $p+q$, where $p$ and $q$ are two positive integers such that $p$ and $q$ have no common factor larger than $1$ and 
$$\frac{1}{20} + \frac{1}{30} + \frac{1}{42} + \frac{1}{56} + \frac{1}{72} + \frac{1}{90} = \frac{p}{q}.$$
By using Wolfram Alpha, I obtain the sum is $\frac{3}{20}$. But I have no idea on how to obtain the sum.
Any hint would be appreaciated. 
[The question is taken from SMO 2015 Junior section]

We can observe that
\begin{align}
20&=4\cdot 5\\
30&=5\cdot6\\
42&=6\cdot7\\
56&=7\cdot8\\
72&=8\cdot9\\
90&=9\cdot10.
\end{align}
Can you use partial fraction?
