1. Determine the coefficient of $x^{3}$ in the expanded form (after the powers have been carried out) of the expression

$$
(1+x)^{3}+(1+x)^{4}+\ldots+(1+x)^{1995}
$$
Solution. According to the formula for the sum of a geometric progression, we get:

$$
(1+x)^{3}+(1+x)^{4}+\ldots+(1+x)^{1995}=\frac{(1+x)^{3}\left[(1+x)^{1993}-1\right]}{x}=\frac{(1+x)^{1996}-(1+x)^{3}}{x}
$$

Since the denominator contains $x$, it is sufficient to determine the coefficient of $x^{4}$ in the numerator. However, $x^{4}$ does not appear in $(1+x)^{3}$, so it is sufficient to determine the coefficient of $x^{4}$ in $(1+x)^{1996}$.

Thus, the desired coefficient is $\binom{1996}{4}$.