#
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
The most recent version

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- Description: collection of exercises on infinite sequences. Serveur Wims de l'ESPE-Nice-Toulon - Université de Nice - Sophia Antipolis
- Keywords: interactive mathematics, interactive math, server side interactivity, analysis, calculus, sequence,convergence, limit