To evaluate the series `sum_(n=2)^oo ln(n),` we may apply
the **divergence test**:

If `lim_(n-gtoo) a_n != 0` then `sum a_n` diverges.

From the given series `sum_(n=2)^oo ln(n)` , we have `a_n=ln(n)` .

Applying the diveregence test,we determine the convergence and divergence of the series using the limit:

`lim_(n-gtoo)ln(n) = oo`

When the limit value (L) is `oo ` then it satisfies `lim_(n-gtoo) a_n != 0 .`

Therefore, the series `sum_(n=2)^oo ln(n)` diverges.

We can also verify this with the graph: `f(n) = ln(n)` .

As the value of `n` increases, the function value also increases and does not approach any finite value of L.

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