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`sum_(n=0)^oo (7/6)^n` Verify that the infinite series diverges

`sum_(n=0) (7/6)^n`


To verify if the series is divergent, apply the Geometric Series Test.


Take note that a geometric series has a form


`sum ar^n`


It converges if `|r|lt1` . And it diverges if `|r|gt=1 ` .


In the series the value of a and r are:


`a=1`


`r=7/6`


Taking the absolute value of r, it yields


`|r|=|7/6|`


`|r|=7/6`


Since `|r|>1` , the series is divergent.

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