applicability: $\mathbb {N, Z, Q, R}$

# Definition: Real Sequence

A real sequence $$(a_n)_{n\in\mathbb N}$$ is a sequence of real numbers $$a_n\in\mathbb R$$.

### Examples

• $(2^n)_{n\in\mathbb N}=(1,2,4,8,\ldots)$
• $(\sqrt{n})_{n\in\mathbb N}=(0,1,\sqrt{2},\sqrt{3},\ldots)$
• $(3)_{n\in\mathbb N}=(3,3,3,3,\ldots)$
• $(\frac{n}{n+1})_{n\in\mathbb N}=(0,\frac{1}{2},\frac{2}{3},\frac{3}{4},\ldots)$
• recursively defined sequences.

Applications: 1
Chapters: 2 3
Corollaries: 4
Definitions: 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Examples: 24
Lemmas: 25 26 27
Proofs: 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55
Propositions: 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73
Sections: 74 75
Theorems: 76 77

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### References

#### Bibliography

1. Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983
2. Forster Otto: "Analysis 2, Differentialrechnung im $$\mathbb R^n$$, Gewöhnliche Differentialgleichungen", Vieweg Studium, 1984