A1 Determine the positive integer $n$ that satisfies the following equation:
$$
\frac{1}{2^{10}}+\frac{1}{2^{9}}+\frac{1}{2^{8}}=\frac{n}{2^{10}} .
$$
Solution
Adding the left hand side of the given equation with with a common denominator of $2^{10}$, we have,
$$
\frac{1}{2^{10}}+\frac{1}{2^{9}}+\frac{1}{2^{8}}=\frac{1}{2^{10}}+\frac{2}{2^{10}}+\frac{2^{2}}{2^{10}}=\frac{1+2+4}{2^{10}}=\frac{7}{2^{10}} .
$$

Therefore, $n=7$.