Analysis I LEARNSHEEtmT
TOPICS
3 NattirlicheZahlen und voustandige Indulation
Vollstoindige Induration
TIFolge Fakultoit Fibonacci Folge
Ft Bernoulli Ungleichung
4 Folgen und ihre Grenzwerte
Beschranktheit tolge
Konvergent Diligent
Sandwichsat 2
TI Rechenregel
Monotone
VOLLSTANDIGE INDUKTION
Indulationsanfang WTF is Vollstandige Induration
IndurationsSchritt eineBeweismethode um HneIN Aussagen
Indulationsbehauptung zu beweisen
Indurationsbeweis
9 HnEIN SeiAchteineAussage in Abhangigheit von n
wenn dies NICHT
gilt dann wird die Indulation nicht funktionieren
Indulationsanfancy
Manzeigt dass n 1 ist
IndurationsSchritt Oder
Man zeigt d s n t 1 gilt e TY man auch zeigen dass n K
gilt
Und dann n Kt1 OPTIONAL
Wenn and erfolgreich Indurationsbehauptung
bewiesen Sind dann ist dieAussage Indurationsbeweis
A n fair jedes n e INWahr
Beispiel
n I
1121 1 n2 2.1 1 12
, Zeigenclass nt1 gilt
mi
htt
112it
Ri 1 Hi1 1 2Intl 1 n2t2n 1
htt
Bernoulli Ungleichung
Ttx 2 1 thx
A O 1 31
A1 Ttx 2 It x
A 211 11122 It 2x
11 2 11122 It 2x
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