`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.