Question

Find the sum of the infinite geometric series, if it exists. 4 - 1 + 1/4 - 1/6 + . . .

A. - 1

B. 3

C. 16/5

D. does not exist

Answer 1

4-1+1/4-1/16+........
a=4,r=-1/4
\[\left| r \right|=\frac{ 1 }{ 4 }<1\]
\[S \infty=\frac{ a }{1-r }=\frac{ 4 }{1-\left( \frac{ -1 }{4 } \right) }\]
\[S \infty=\frac{ 4 }{ 1+\frac{ 1 }{ 4 } }=\frac{ 4 }{\frac{ 4+1 }{ 4 } }=4\times \frac{ 4 }{ 5 }\]
\[S \infty=\frac{ 16 }{5 }\]

Answer 2

thank you for explaining @surjithayer ;-)