Question

How do you determine if `Sigma (2n-3)/(5n+6)` from `n=[0,oo)` converge and find the sums when they exist?

Answer 1

The sum diverges.

Explanation:

Sum of an infintite series `sum_(n=0)^ooa_n` converges only if `lim_(n->oo)a_n=0`.

In this question, `lim_(n->oo)(2n-3)/(5n-6)=2/5≠0` and the sum diverges to infinity.