Answer
$\sum_{i=1}^{18}\dfrac{i}{i+2}$
Work Step by Step
Given: $\dfrac{1}{3}+\dfrac{2}{4}+\dfrac{3}{5}+...+\dfrac{18}{20}$
we can see that the consecutive numbers for numerators starts and lasts from $1$ to $18$ and the consecutive numbers for denominators starts and lasts from number $3$ to $20$.
This means that the numbers must be shown by a summation symbol as written as:
$\dfrac{1}{3}+\dfrac{2}{4}+\dfrac{3}{5}+...+\dfrac{18}{20}=\sum_{i=1}^{18}\dfrac{i}{i+2}$
