Question

Determine whether the geometric series is convergent or divergent. And if it is convergent, what is the sum?

Answer 1

\[\sum_{n=1}^{\infty} \frac{ (-3)^{n-1} }{ 4^{n} }\]

Answer 2

i just don't know which value a and r is.

Answer 3

what are our criteria for convergence? and the r will be the part that his the exponent

Answer 4

\[\frac{(-3)^{n-1}}{4^n}\]
\[\frac{(-1)^{n-1}~{3^n}~3^{-1}}{4^n}\]
etc ...

Answer 5

you kinda of lost me here.

Answer 6

i know for convergence, r needs to be less than 1

Answer 7

convergence is when r is between -1 and 1

Answer 8

yeah, but im not sure how to figure ou how to find r.

Answer 9

well let c n1= 1/4 right?

Answer 10

?