Geometric series strange answer

Question

I am new to geometric series and approached this question with the general form:

(scale-factor * $common-ratio^{n+1}$ -1) / (common-ratio - 1)

n = 10

i = 1

$(3^i)/(2^i)$

$3^i \to (3^{11} -1)/2$

$2^i \to (2^{11} -1)/1$

so i got 88573/2047

= 43.27 (2dp)

which i thought was a bit low since I checked $3^{10}/2^{10} = 57.67$ (2 dp). Am I looking at this geometric series incorrectly or am i just being paranoid about this answer?

Answer 1

$$\sum_{i=0}^{10}\left(\frac32\right)^i=\frac{\left(\frac32\right)^{11}-1}{\frac32-1}$$

and $$\sum_{i=0}^{10}\left(\frac32\right)^i\ne\frac{\sum_{i=0}^{10}3^i}{\sum_{i=0}^{10}2^i}$$