How do you test the alternating series #Sigma (-1)^n(2^n+1)/(3^n-2)# from n is #[0,oo)# for convergence?
The series is convergent.
A sufficient condition for an alternating series to converge is established by the Leibniz test stating that if:
then the series is convergent.
In our case:
so the first condition is satisfied.
and it follows that:
Thus also the second condition is satisfied and the series os convergent.