Question

The series 2/3+3/4+4/5 is divergent T or F

Answer 1

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.