Endpoint Analysis - McLauren Series

[sunburnt]

Hello there.

A function f is defined by: f(x) = 1/3 + 2/3²x + 3/3³x² + ... + (n + 1) / (3^{n + 1}) * xⁿ

I have found the interval of convergence of this McLauren series to be 3 ( i.e. -3 < x < 3) however, I am a little rusty on endpoint analysis. Can anyone help me determine whether or not -3 and/or 3 should be included? I plugged -3 into the function and came up with

1/3 - 2/3 + 1 - 4/3 ...
The signs alternate, however the values don't decrease, so I'm hesitant to say that it converges by the alternating sign test. It fails the Nth term test...

When I put in 3 I got...
1/3 + 2/3 + 1 + 4/3 which obviously doesn't converge.

Heeelp!