"Just please write down the maths and I will understand through my course."
With respect, I don't think the maths as such is the issue for you. Both the above explanations give the maths. I'm just guessing but it seems to me you are not focussing on the right thing here — it's as if you think, "If only someone would write down the right formula for me then I would get it."
The point is that R is a DEFINED vector—it is defined by the equation given—but the real question is WHY is it defined that way, i.e. what is its intended meaning? I think that's what you are, or should be, trying to get at, and not just some mathematical expression that would seem to switch a light on for you.
The way to see this is to start with a very simple example, say of two particles with identical masses. Look at where R (as defined) is in relation to these — right in the middle, between them. Now vary one of the masses, double it say, and see where that puts R. To put it very loosely, in both cases it's the pivot point about which the particles would exactly balance.
Now extend this to three particles. You could make them co-linear to start with then move one out of line to form a plane triangle. But in each case look at the resulting R (as defined) and see that it is indeed the 'balance point'. 359
You don't HAVE to do all this by drawing diagrams and writing equations but do so if it helps. Otherwise you could just do it in your head. But do it in whatever way makes you feel comfortable.
Now turn this whole exercise on its head and ask yourself: how would I go about finding such a 'balance point' for a general set of particles; what property is it of this 'balance point' that DEFINES it and tells me where it is? You'll find the answer is precisely the formula given. And that's really is the point (issue) here.
The general idea is that you make things as conceptually simple for yourself as possible until you 'get it'. For example, if necessary imagine the particles are fixed in a massless gel so that they cannot move. That kind of thing.
Of course, having said all that, I might be completely wrong in my view of your current mindset. Dunno. But that's my best guess. I hope it helps. 499