Remainders and short sums

Write tools that expand a power term by term, find a remainder from two terms, and add the first terms of $(1 + h)^n$.

The idea. The terms of $(a + b)^n$ are ${}^{n}C_{k}\,a^{n - k}\,b^{k}$. Modulo $d^2$, $(d + 1)^n$ behaves like $1 + nd$. For small $h$, the first few terms of $(1 + h)^n$ are close to the whole value.

Your tasks.

1. In terms, return the list of the $n + 1$ terms of $(a + b)^n$, as whole numbers.
2. In remainder_mod_square, return the remainder of $(d + 1)^n$ divided by $d^2$, using only $1 + nd$.
3. In short_sum, return the sum of the first count terms of $(1 + h)^n$.