what exactly is a recursive series? (how to define or explain it)?

Answer 1

Recursive series: a series where each term in the series is defined in terms of previous terms in the series. Examples:

Fibonacci series: 1, 1, 2, 3, 5, 8, 13, 21... in general, the nth term in the series is defined as the sum of the (n-1)th and (n-2)th term.
Factorial series: 0!=1, n!=n*(n-1)!

Which leads me to an old joke I saw in a dictionary once:

Recursion (n): see recursion.

Answer 2

A function which is defined in terms of itself is called a recurive function or a series. It must have a terminating comdition

like for factorial

fact(0) = 1; fact(n) = n* fact(n-1) n >0

fibonacci series

f(0) = 0; f(1) = 1;
f(n) = f(n-1) + f(n-2) n >1

Answer 3

All geometric and arithmetic series are recursive. This means that each term is defined in terms of the previous term.