Question

PLEASE HELP! :( what is the sum of the geometric series


15

E 2(1/3)^3

x = 0


rounded to the nearest whole number???

A) 1
B) 2
C) 3
D) 4

the picture is attached! i don’t get it please help!

Answer 1

The sum of a geometric series is
$S_n = a(\frac{1-r^n} {1-r}),r≠1$

In this case,
$a(1) = a = 2(\frac{1}{3})^0 =2 \\ a(2) = 2(\frac{1}{3})^1 =\frac{2}{3}$
Then,
$r=\frac{a(2)} {a(1)} =\frac{\frac{2} {3} } {2} =\frac {1 } {2 }$
We'll get the result,
$S_{15} =(2)(\frac{1-(\frac{1} {3} )^{15}} {1-\frac{1} {3}}) \\ = (2)( \frac{1}{ \frac{2}{3} } ) \\ = (2)( \frac{3}{2} ) \\ = 3$

The answer is C

Note, $( \frac{1}{3} )^{15}$ is close to zero.