Question

What is convergent and divergent in sequences and series in mathematical lession.

Answer 1

A series is said to be convergent, if it converges to a value as the terms of series tends to infinity.
A series is said to divergent, it it does not converge to a value but keeps on either increasing or decreasing as the terms of series tends to infinity.
Simple examples are :
Series of terms which are square of number : 1, 4, 9, 16, 25, 35... tends to infinity
Series of terms which are reciprocal of the number : $1,\frac{1}{2},\frac{1}{3},\frac{1}{4},\frac{1}{5}$,which ultimately tends to 0 as the terms tend to infinity.
You can see the behaviour of these series in the graphs below: