The double integral dx dy is an improper integral and could be defined as the limit of

Question:

The double integral dx dy — ху Jo Jo 1 dx dy is an improper integral and could be defined as the limit of double integrals over the rectangle [0, t] x [0, t] as t → 1-. But if we expand the integrand as a geometric series, we can express the integral as the sum of an infinite series. Show that o Jo 1 — ху dx dy = E n-1 n-1 n |-|1*