Question

silly question, but how does this converge & not diverge?

Answer 1

alternating series test,

Answer 2

it converges since the common ratio is -1/3

and if -1 < r < 1 then the geometric series converges

Answer 3

http://tutorial.math.lamar.edu/Classes/CalcII/AlternatingSeries.aspx

\[\sum_{0}^{inf} (-1^n)\frac{ 1 }{3^n } \] change it to a limit and and as 1/3^n approach inf it become 0
1/3^n is decreasing