Question 1040821
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This is a geometric series of the form {{{a*r^n}}} where n is a whole number. 


In this case, {{{a = 1/3}}} and {{{r = -4/3}}}


The rule is this: an infinite geometric series converges to a fixed number if and only if {{{-1 < r < 1}}}


But because {{{r = -4/3 = -1.33}}} (approx) is NOT in the interval {{{-1 < r < 1}}}, this means that the infinite geometric series does NOT converge.


So the geometric series *[Tex \LARGE \sum_{k=1}^{\infty}\frac{1}{3}\left(-\frac{4}{3}\right)^k] <font color=red size=4>diverges</font>. It will not approach a fixed number>
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