Let A = _i=1^10_j=1^10i,j and B = _i=1^10_j=1^10i,j.

Question

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

Answer: 1100

Accepted Answer

Since $\min\{i,j\}+\max\{i,j\}=i+j$ always,
$$A+B = \sum_{i=1}^{10}\sum_{j=1}^{10}(i+j) = 10\sum_{i=1}^{10}i+10\sum_{j=1}^{10}j = 10(55)+10(55) = 1100.$$

Solutions · 1