Answer:
[tex]1023[/tex]
Step-by-step explanation:
The formula is
[tex]S_n = \frac{a(1 - {r}^{n}) }{1 - r} [/tex]
The given series is:
[tex]1 + 2 + 4 + 8 + ... + a_{10}[/tex]
where the first term is a=1 and the common ratio is
[tex]r = \frac{2}{1} = 2[/tex]
We plug in all these values to get:
[tex]S_{10} = \frac{1(1 - {2}^{10}) }{1 - 2} [/tex]
[tex]S_{10} = \frac{1 - 1024}{ - 1} = 1023[/tex]
