The geometric series [tex]\sum\limits^{\infty}_{n=1} -4(-\frac 12)^{n-1} = -\frac 83[/tex] converges
How to determine the series type?
The series is given as:
[tex]\sum\limits^{\infty}_{n=1} -4(-\frac 12)^{n-1} = -\frac 83[/tex]
The above series is a geometric series with the following common ratio
[tex]r = -\frac 12[/tex]
Series that have a common ratio whose absolute value is less than 1 would converge.
i.e.
|r| < 1
Because |-1/2| < 1, then we can conclude that the series would converge
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