[sweetjesus]

when I read it it wasn't clear to me either, so I looked at what was written and saw that the fractions on the right side were clearly getting smaller and smaller fast because each successive denominator consisted of the multiplication of a clearly increasing number of clearly increasingly large integers so within a matter of seconds it was clear to me that within that small number of terms that each additional term would have a vanishingly small effect on the (alternating sign) summation so what they said was had to be true.

So, I do sympathize with your overall point, but this isn't really a good example of it. It's less clear to me what they said about the left side of the (in)equality because that expression to me is much more eye-glazing...but it doesn't take long to convince yourself of that one too. I think it's fair for them to say it's "clear", but you have to not let yourself be put off by the large number of algebraic symbols strung together.