Polymer Chemistry NMR question
I hope this is not a homework question. Suppose your polymer has $n$ reapeating units and capped with methyl groups at the end as you described. Thus, it should looks like following figure:


Thus it has $n$ $\ce{(-CH2CH2-)}$ units and $2$ $\ce{(-CH3)}$ units. Thus your $\ce{(-O-CH2-)}$ signal is accounted for $4n$ protons while $\ce{(-O-CH3)}$ signal accounted for only $6$ protons. Thus,
$$\frac{4n}{6} = \frac{20}{1}$$
You may find the value of $n$ from this equation and you can calculate the molecular weight of the polymer in hand.