Answer
See below.
Work Step by Step
See text: sec.3, corollary to Th.6.
A series $\displaystyle \sum_{n=1}^{\infty}a_{n}$ of nonnegative terms converges if and only if
its partial sums are bounded from above.
If a series has only nonnegative terms, then the sequence of its partial sums is nondecreasing. Now, Theorem 6, which deals with bounded monotonic sequences, applies.
As does the above corollary.
If we do determine that such a series is convergent, but there is no formula to calculate the actual sum, we may approximate the sum with a partial sum, given allowed error margins.
