The given geometric sequence is $4, 2, 1, \dots$, where:

• The first term $a = 4$,
• The common ratio $r = \frac{2}{4} = \frac{1}{2}$.

The formula for the sum $S_n$ of the first $n$ terms of a geometric sequence is:

$S_n = \frac{a(1 - r^n)}{1 - r} \quad \text{for} \, |r| < 1.$

Here:

• $a = 4$,
• $r = \frac{1}{2}$,
• $n = 10$.

Substituting these values:

$S_{10} = \frac{4 \left(1 - \left(\frac{1}{2}\right)^{10}\right)}{1 - \frac{1}{2}}.$

Simplifying:

[ S_{10} = \frac{4 \left(1 - \frac{1}{1024}\right)}{\frac{1}{2}} = \frac{4 \left(\frac{1023}{1024}\right)}{\frac{1}{2}} = 4 \times \frac{1023}{1024} \times