I have no idea on how to approach this?
$$ \sum_{i=1}^{n}\sum_{j=1}^{m}a_i + a_j = \sum_{i=1}^{n} a_i + \sum_{i=1}^{m} a_j (it \space may \space be \space wrong \space it \space is \space just \space an \space example) $$
Any hint on induction?
I think the base case is showing n+m = 2
then the induction hypothesis is some thing like this? $$ \sum_{i=1}^{n+1}\sum_{j=1}^{m+1}a_i + a_j = \sum_{i=1}^{n+1} a_i + \sum_{i=1}^{m+1} a_j $$