# Tagged: Theorems

## Real Sequences

Sequence of real numbers A sequence of real numbers (or a real sequence) is defined as a function $f: \mathbb{N} \to \mathbb{R}$ , where $\mathbb{N}$ is the set of natural numbers and...

## Set Theory, Functions and Real Number System

SETS In mathematics, Set is a well defined collection of distinct objects. The theory of Set as a mathematical discipline rose up with George Cantor, German mathematician, when he was working on some problems...

## Fermat Numbers

Fermat Number, a class of numbers, is an integer of the form $F_n=2^{2^n} +1 \ \ n \ge 0$ . For example: Putting $n := 0,1,2 \ldots$ in $F_n=2^{2^n}$ we get...

## D’ ALEMBERT’s Test of Convergence of Series

Statement A series $\sum {u_n}$ of positive terms is convergent if from and after some fixed term $\dfrac {u_{n+1}} {u_n} < r < {1}$ , where r is a fixed number....