Summation Skip Notation The following notation means to sum 1 to N:
$$\sum_{n=1}^N n$$
Is there a notation to not increment by one for each step, but, say, 10?

As long as you have a constant skip size, you can handle it by multiplying the subscript by the skip size wherever it appears inside the summation: in your example you’d get
$$\sum_{n=1}^N10n\;.$$
Of course that gives you the sum of all $N$ values from $10$ through $10N$. If you wanted just the sum of those multiples of $10$ that are no bigger than $N$, you’d have to adjust the upper limit:
$$\sum_{n=1}^{\lfloor N/10\rfloor}10n\;.$$
If you wanted to start with $n=1$ and increase in steps of $10$, for a total of $N$ terms, it would be
$$\sum_{n=0}^{N-1}(1+10n)\;.$$
And if you wanted to start with $n=1$ and increase in steps of $10$ up through a maximum value of $N$, it would be
$$\sum_{n=0}^{\left\lfloor\frac{N-1}{10}\right\rfloor}(1+10n)\;.$$
