This is how I do it (not my Idea, forgot who posted the tutorial); I can't guarantee it will work with any dropbox version (or indeed, anywhere at all; maybe I'm unique after all).
First, right-click the image in the dropbox folder, select 'copy dropbox link' ('Dropbox-Link kopieren' in German, maybe it's formulated differently elsewhere, it's the ninth item on the dropdown menu on my PC) and left-click as usual.
If you paste the link, it would look like this:
https://www.dropbox.com/s/cutymssqpc8n9 ... 4.png?dl=0
That one has never worked; no image will be shown.
But if you replace the blue part of the link
with the following
so the link now looks like this
https://dl.dropboxusercontent.com/s/cut ... 4.png?dl=0
the image should be shown:
Hopefully nobody at dropbox reads this post.