Question

The Sum of the Series :
\[\frac{ 1 }{ 2 }-\frac{ 3 }{ 2^2 }+\frac{ 1 }{ 2^3}-\frac{ 3 }{ 2^4 }+......+\infty \]

Answer 1

@satellite73 @mahmit2012 @asnaseer @eigenschmeigen

Answer 2

Split the series
\[(\frac 1 2 +\frac 1 {2^3}+....)-3(\frac 1 {2^2}+ \frac 1 {2^4}...)\]
Now these both are infinite Geometric series. Could you find the sum of each ?

Answer 3

if you factor out another 1/2 from the negative series you should spot something

Answer 4

break in to two parts

Answer 5

oh, what everyone else said, sorry

Answer 6

(2-3)*geo series