LINQ

using System;
using System.Collections.Generic;
using System.Linq;

public static class Series
{
    public static IEnumerable<string> Slices(string input, int length)
    {
        if (length < 1 || length > input.Length)
            throw new ArgumentException("Invalid length");

        return Enumerable.Range(0, input.Length - length + 1)
            .Select(i => input.Substring(i, length));
    }
}

The first step is to check the input for validity:

if (length < 1 || length > input.Length)
    throw new ArgumentException("Invalid length");

Then we use Enumerable.Range() to create the sequence of integers that represent the index from which we want to retrieve an individual slice:

Enumerable.Range(0, input.Length - length + 1)

The tricky thing is to determine which indexes to return. Let's look at an example input and some different slice lengths to examine which slice indexes we want to be getting the slice from:

From this table, we can see the first slice index is always 0 and that input length - slice length + 1 indexes are used. Therefore, the Enumerable.Range() call starts at 0 and has returns input.Length - length + 1 elements.

The final step is to map the indexes to the slices, for which we use Select() and the Substring() method:

Select(i => input.Substring(i, length))

The value we're returning is the substring of the input that starts at index i and which has length equal to length.

Shortening

The Substring() call could be replaced with a range call:

input[i..(i + length)]

While slightly shorter, the fact that the parentheses are required makes this a minor gain. In this case, the Substring() call probably better captures the domain logic, as it is more clear that we're return a string of size length.