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,

`image`
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)( (1)/( (2)/(3) ) ) \\ = (2)( (3)/(2) ) \\ = 3`

The answer is C

Note,
`( (1)/(3) )^(15)` is close to zero.