Summation Skip Notation

You could just write: $$ \sum_{k = 1}^{N/10} 10 k $$ Another option is to write conditions under the sum sign: $$ \sum_{\substack{1 \le n \le N \\ 10 \mid n}} n $$

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

$$\sum_{n=0}^{\left\lfloor\frac{N-1}{10}\right\rfloor}(1+10n)\;.$$