Question

How do you find the sum of the convergent series 3-9+27-81+... If the convergent series is not convergent, how do you know?

Answer 1

The given series does not converge.

Explanation:

The series `3, -9, +27, -81, ...`
has a ratio of `r=(-3)` (i.e. `a_(i+1) = a_ixx(-3)` )

A geometric series only has a convergent sum if
`color(white)("XXX")abs(r) < 1`