Question

Compute each of the double double sums below

(a)3∑(i=1) 2∑(j=2) (i+j)

(b)3∑(i=0) 2∑(j=0) (2i+3j)

Answer 1

(a)

$$\sum_{i=1}^{3}\sum_{j=2}^{2}( i+j) =\sum_{i=1}^{3}(i+2)$$ $$=1+2+2+2+3+2=12$$

(b)

$$\sum_{i=0}^{3} \sum_{j=0}^{2} (2i+3j)$$ $$= \sum_{i=0}^{3}( 2i+(2i+3)+(2i+6))$$ $$= \sum_{i=0}^{3}( 6i+9)$$ $$=9+6+9+6\cdot2+9+6\cdot3+9$$

$$=72$$