Find the largest sum of any slice inside an array
Two minor remarks:


For consistency sake, this

accumulator = maxLastPair &gt; accumulator + addend ? maxLastPair : accumulator + addend;


can be implemented similar to the other statements as 

accumulator = Math.Max(maxLastPair, accumulator + addend);

Some comments would be welcome in the loop. What exactly is the idea behind the different variables you keep. It took me a while to convince myself that your method was working as it should.