Identify whether the series is a convergent or divergent geometric series and find the sum, if possible. (2 points)

Question

Identify whether the series   is a convergent or divergent geometric series and find the sum, if possible. (2 points)

campbell_st · Answer

find the common ratio. 

if 

$$-1 < r < 1$$

then the series is convergent

if its convergent you can use the infinite sum formula 

$$S_{\infty} = \frac{a}{1 - r}$$

hope it helps

anonymous · Answer

Summation from 1 to infinity 16(5)^
$$\sum_{1}^{\infty}16(5)^{i-1}$$i-1

campbell_st · Answer

ok... well this will be divergent... 

look at the pattern of terms    

i = 1      16

i = 2      80

i = 3      400

etc... so  since r > 1 the series is divergent