as integram 1 Lady dxdy 1 xy 0 0 is an improper integral and could be defined as the limit of double integrals over the rectangle 0 t 0 t 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 int 0 1 int 0 1 frac 1 1 x y d x dy sum n 1 infty frac 1 n 2