Question

Does the series converge or diverge? If it converges, what is the sum? Show your work.
http://postimg.org/image/obo9tkwr5/

Answer 1

\[r=-\frac{ 1 }{ 2 },\left| r \right|=\left| -\frac{ 1 }{ 2 } \right|=\frac{ 1 }{ 2 }<1\]
\[r^n \rightarrow 0~ as~ n \rightarrow \infty\]
so series converges
\[S _{\infty}=\frac{ a }{ 1-r }=\frac{ -4 }{ 1-\left( -\frac{ 1 }{ 2 } \right) }=\frac{ -4 }{ \frac{ 3 }{ 2 } }=-\frac{ 8 }{ 3 }\]

Answer 2

gracias~