times -1/2 each time
common ratio is -1/2
|-1/2|<1 so the series converges
the sum of an infinite geometric sequence when the common ratio is r and the first term is a1 is [tex]S=\frac{a_1}{1-r}[/tex]
the first term is 1/2 and r=-1/2
[tex]S=\frac{\frac{1}{2}}{1-\frac{-1}{2}}[/tex]=
[tex]S=\frac{\frac{1}{2}}{1+\frac{1}{2}}[/tex]=
[tex]S=\frac{\frac{1}{2}}{\frac{3}{2}}[/tex]=
[tex]S=(\frac{1}{2})(\frac{2/3})[/tex]=
[tex]S=\frac{2}{6}[/tex]=
[tex]S=\frac{1}{3}[/tex]=
the sum of the infinite geometric sequence is 1/3
