High number_ Chapter 6 infinite series__ Properties of positive series

The convergence and divergence of positive series should be judged , You can do this by

1.   Comparative discrimination

The core idea ： Large series converge , Small series also converge ,

Small series divergence , Large series also diverge .

Look at an example

2. Root value discrimination

Be careful 3 Theorem ：1. When x>0 when ,   sinx < x.
                        2. When x —>0 when ,  1- cosx ≈ x² / 2.

                        3. When x —>0 when ,  sinx ≈ x.