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How to Evaluate the equation in the picture, not sure what to do with the infinity

How to Evaluate the equation in the picture not sure what to do with the infinity class=

Respuesta :

LammettHash
Recall that for an infinite geometric series of the form

[tex]\displaystyle\sum_{n=0}^\infty ar^n[/tex]

as long as [tex]|r|<1[/tex], the series converges to the value [tex]\dfrac{a}{1-r}[/tex].

Here you have [tex]r=-\dfrac23[/tex], so the series converges. You have

[tex]\displaystyle\sum_{n=0}^\infty 5\left(-\dfrac23\right)^n=\dfrac5{1-\left(-\dfrac23\right)}=3[/tex]

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