If we're talking about series, we're talking about a summation.
This is a geometric series, so we will be using the sum to n terms of a geometric series given by:
[tex]S_n = \frac{a(1 - r^{n})}{1 - r}[/tex], where a is the first term, r is the common ratio, and n is the number of terms.
Now, we know the first term is 4.
We know the ratio is [tex]-\frac{1}{2}[/tex]
And we are finding to the 10th term.
Plugging everything into the equation:
[tex]S_10 = \frac{4[1 - (-\frac{1}{2})^{10}]}{1 + \frac{1}{2}}[/tex]
After this, we get: 2.6640625... ≈ 2.66 (ie D)
