How do i calculate sqrt n i
Next page:Limits of functions and Upwards:Completeness of the real numbers Previous page:Monotonous consequences & nbsp content
Comment: As a starting value you can e.g. choose. Then .
Proof. The estimates follow by induction .
- The first two statements are clear by definition.
- There follows after Bernoulli (): ...
Description. The uniquely determined number from the previous sentence is called the -th root . Description: One sets .
- Be there . If , then . Out so follows .
- The existence of the nth root follows from the determination .
For , , and applies:
Proof. We sit
If we apply the inequality just shown, it follows:
Proof. The case is clear. If the limit so there is a so that
Comment: The convergence follows from Bernoulli's inequality: For applies:
Proof. For put one
In the event of is and from
In the event of are the reciprocal values strictly monotonically falling.
Comment. The claims follow from the estimate
Proof. According to Lemma applies
Next page:Limits of functions and Upwards:Completeness of the real numbers Previous page:Monotonous episodes & nbsp content Analysis1-A. Lambert 2001-02-09
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