Question

What is the sum of the geometric series 2^0 + 2^1 + 2^2 + 2^3 + 2^3 + 2^4 + … + 2^9?

Answer 1

Hello,

$1+2+2^2+2^3+...+2^9=\frac{2^{10}-1}{2-1}=1023$

Answer 2

the nth term is
an=a1(r)^(n-1)
an=1(2)^(n-1)
a1=1
r=2

the sum of a geometric seequence is
$S_{n}=\frac{a_{1}(1-r^{n})}{1-r}$
a1=1
r=2
we want to find $S_{10}$ (since we minus 1, the highest exponet is 9 so add 1 to make it correct)

$S_{10}=\frac{1(1-2^{10})}{1-2}$
$S_{10}=\frac{(1-1024}{-1}$
$S_{10}=\frac{(-1023}{-1}$
$S_{10}=1023$