Evaluate the double sum S=∑p=1∞∑q=1∞1pq(p+q+2)S = \sum_{p=1}^{\infty} \sum_{q=1}^{\infty} \frac{1}{p q (p+q+2)}S=∑p=1∞∑q=1∞pq(p+q+2)1.
74\frac{7}{4}47
78\frac{7}{8}87
34\frac{3}{4}43
98\frac{9}{8}89