True, the series is indeed divergent.
The n-th term is given by
(n + 1) / (n + 2)
starting with n = 1, so that
(n + 1) / (n + 2) = (n + 2) / (n + 2) - 1 / (n + 2) = 1 - 1 / (n + 2)
and as n grows to infinity, the rational term vanishes, the summand converges to 1, and the sum behaves like ∑ 1, which diverges.
