1. Set . Then (j - k) is even.

2. Checkall 5 terms, replacing j by k + 2m. For instance:

..... j+2k isonlyeven if k is even because then j is even too.

...

..... (jk + j) is even if k is even because then the 1st bracket would be even too; (jk + j) is even if k is odd because then the 2nd bracket would be even too. A product is even if one factor is even.