My calc. AB teacher decided against teaching Riemann sums with sigma notation and as I have been studying BC independently I sort of came up with this problem. The answer is pi of course, but if I use the sigma notation and add "infinite rectangles" I need to have some way of coming up with interval widths in a different manner than the normal (b-a)/n. the largest problem seems to be that I don't know how to figure out how to evaluate this type of integral where the width changes. On top of this I know pi is irrational so I figure my answer should come out to an irreducible infinite series but I haven't a clue how to come to that point using these riemman sums. Definite integration is not much problem, I can use arcsin and tables I think, I just want to better understand this method and my teacher hasn't taught anything above math heuristics for a long time. Thanks!