Question

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

Answer 1

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

Answer 2

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

Answer 3

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