- #1

Briggs

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For example, Find the values of x for which the following geometric series converge

I have done the first one easy enough

[tex]2+4x+8x^2+16x^3...[/tex]

[tex]r=2x[/tex]

[tex]|r|<1[/tex]

[tex]|x|<\frac{1}_{2}[/tex]

[tex]\frac{-1}{2} < x < \frac{1}_{2}[/tex]

But then it gets more difficult and adds more to the question for example

[tex]5+25(3x+4)+125(3x+4)^2[/tex]

I get [tex]r=5(3x+4)[/tex]

so [tex]|5(3x+4)|<1[/tex]

But then I am stuck as to what to do next any hints on how to go about these questions would be appreciated.