Mathematical notation - cummulative summation The Mertens function can be calculated in _Mathematica_ by: Accumulate[Table[MoebiusMu[k], {k, 1, n}]] and is written as $$M(n)=\sum_{k=1}^n\mu(k)$$ Could someone please tell me how I would write Table[Mean[Accumulate[Table[MoebiusMu[k], {k, 1, n}]]], {n, 1, x}] in mathematical notation?

Here is how `Accumulate` works: `Accumulate[{a, b, c, d}]` produces


{a, a + b, a + b + c, a + b + c + d}


Thus, the `m`th entry of the list `Accumulate[Table[MoebiusMu[k], {k, 1, n}]]` is $$M(m)=\sum_{k=1}^m\mu(k)$$ so that `Mean[Accumulate[Table[MoebiusMu[k], {k, 1, n}]]]`, the average of the `n` entries on this list, is the just average of the first $n$ values of the Mertens function $M(k)$: $$\frac{1}{n}\left(\sum_{k=1}^nM(k)\right)\qquad$$ and then the outer `Table` just makes a list of these values from `n=1` to `n=x`.