Exercise 5, § 7

General Topology, IV, 398

Let $(d_n)$ be a sequence of finite real numbers $\geq 0$ such that

\sum_{n=0}^{\infty} d_n = + \infty.

What can be said about the convergence of the series whose general terms are

\frac{d_n}{1 + d_n}, \quad \frac{d_n}{1 + nd_n}, \quad \frac{d_n}{1 + n^2 d_n}, \quad \frac{d_n}{1 + d_n}?

Solution

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