Words and Concepts

Question 1

Divergent series

Answer 1

Adding up all elements in an infinte sequence gives us an infinite series, if the sequence goes to infinity then certainly the series will also go to infinity. The limit of this sequence will go to infinity, and so will the series.

Question 2

Sequences

Answer 2

An infinite sequence should not be confused with an infinite series, which involves adding the numbers instead of listing them.

A sequence is a list of numbers or actually a function whos domain is the natural numbers

Before the value of N the sequence can jump around all it wants, but after it goes past N (which is on the x axis (in the domain)) the function range has to stay with in the range of Epsilon

Manipulate |f(n)-L|<Epsilon>N
We will find a real number(envolving epsilon), and by the archemedian principle we will say that there will be a number N bigger than that</Epsilon>