#
OEF Sequences
--- Introduction ---

This module actually contains 16 exercises on infinite sequences:
convergence, limit, recursive sequences, ...

### Two limits

Let () be an infinite sequence of real numbers. If one has and for , what can be said about its convergence? (You should choose the most pertinent consequence.)

### Comparison of sequences

Let () and () be two sequences of real numbers where () converges towards . If one has , what can be said about the convergence of ()? (You must choose the most pertinent consequence.)

### Growth and bound

Let () be a sequence of real numbers. If () is , what can be said about its convergence (after its existence)?

### Convergence and difference of terms

Let be a sequence of real numbers. Among the following assertions, which are true, which are false? - If , then .
- If , then .

### Convergence and ratio of terms

Let be a sequence of real numbers. Among the following assertions, which are true, which are false? - If , then .
- If , then .

### Epsilon

Let be a sequence of real numbers. What does the condition imply on the convergence of ? (You must choose the most pertinent consequence.)

### Fraction 2 terms

Compute the limit of the sequence (*u*_{n}), where

### Fraction 3 terms

Compute the limit of the sequence (*u*_{n}), where

### Fraction 3 terms II

Compute the limit of the sequence (*u*_{n}), where
**WARNING** IN this exercise, approximative replies will be considered as false! Type `pi` instead of 3.14159265, for example.

### Growth comparison

What is the nature of the sequence (*u*_{n}), where
?

### Monotony I

Study the growth, sup, inf, min, max of the sequence (*u*_{n}) for *n* , where
. Write for a value that does not exist, and or `-` for + or -.

### Monotony II

Study the growth, sup, inf, min, max of the sequence (*u*_{n}) for *n* , where
. Write for a value that does not exist, and or `-` for + or -.

### Powers I

Compute the limit of the sequence (*u*_{n}), where

### Powers II

Compute the limit of the sequence (*u*_{n}), where
Type `no` if the sequence is divergent.

### Recursive function

The sequence
such that
is a recursive sequence defined by
for a certain function
. Find this function.

### Recursive limit

Find the limit of the recursive sequence
such that

**This page is not in its usual appearance because WIMS is unable to recognize your
web browser.**
Please take note that WIMS pages are interactively generated; they are not ordinary
HTML files. They must be used interactively ONLINE. It is useless
for you to gather them through a robot program.

- Description: collection of exercises on infinite sequences. This is the main site of WIMS (WWW Interactive Multipurpose Server): interactive exercises, online calculators and plotters, mathematical recreation and games
- Keywords: wims, mathematics, mathematical, math, maths, interactive mathematics, interactive math, interactive maths, mathematic, online, calculator, graphing, exercise, exercice, puzzle, calculus, K-12, algebra, mathématique, interactive, interactive mathematics, interactive mathematical, interactive math, interactive maths, mathematical education, enseignement mathématique, mathematics teaching, teaching mathematics, algebra, geometry, calculus, function, curve, surface, graphing, virtual class, virtual classes, virtual classroom, virtual classrooms, interactive documents, interactive document, analysis, calculus, sequence,convergence, limit