Let $A=\sum_{i=1}^{10} \sum_{j=1}^{10} \min \{i, j\} \quad$ and $B=\sum_{i=1}^{10} \sum_{j=1}^{10} \

Question

Let $A=\sum_{i=1}^{10} \sum_{j=1}^{10} \min \{i, j\} \quad$ and $B=\sum_{i=1}^{10} \sum_{j=1}^{10} \max \{i, j\}$. Then $A+B$ is equal to

Professor PC Thomas Classes · Answer

(1100) : $A=\sum_{i=1}^{10} \sum_{j=1}^{10} \min (i, j)$,\ $B=\sum_{i=1}^{10} \sum_{j=1}^{10} \max \{i, j\}$\ $	herefore A+B=\sum_{i=1}^{10} \sum_{j=1}^{10}(i+j)=\sum_{i=1}^{10}(10 i+55)$\ $=10 	imes 55+55 	imes 10=1100$\