real analysis – What unary operation on sequences produces the sequence of pairwise sums?

Given a sequence $(a, b, c,…)$:

  • The partial difference operator produces the sequence $(b-a, c-b, …)$, and
  • The partial summation operator produces the sequence $(a, a+b, a+b+c, … )$

According to a section in the Wikipedia page on series.

What about the sequence $(a+b, b+c, c+d, …)$?

Is there a formal name for the operator that produces this one?