Granice i szeregi

Granice i szeregi Nano: Czy ktoś jest w stanie sprawdzić mi czy dobrze zrobiłam? Podaję link : https://drive.google.com/folderview?id=10Rgq9k1UNkyLYaxWhJdAnRy16FClKX2j Dwóch przykładów nie zrobiłam, nie wiem jak ugryźć. Jakieś wskazówki?

ABC: nie chce być niegrzeczny ale straszne herezje tam są emotka

w tym 7) np. nie znasz wzoru na sumę nieskończonego szeregu geometrycznego zbieżnego? nie budzi twoich podejrzeń że suma dodatnich składników wychodzi ci zero?

Nano: Okej, to w takim razie napisz mi co mam źle. Nie wiem o co chodzi w szeregach, bo nam wykładowca tego nie wytłumaczył tylko dał przykłady i zróbcie.

Nano: Łatwo mówić jak się wszystko już dobrze rozumie. emotka

Nano: Zresztą wykładowca kazał nam ten 7 rozłożyć na właśnie te dwa ułamki

jc: A co to jest 0.1111111... ? może też zero? A może jednak więcej niż zero?

ABC: a ćwiczeniowiec za co wypłatę bierze? zagonić go do roboty niech tłumaczy a jak nie chce donos do rektora i się nowy lepszy znajdzie emotka

Nano: To forum jest od tego, żeby komuś pomóc, a nie podwyższac poczucie własnej wartości. Zrobiłam błędy−zdarza się. Mam prawo czegoś nie rozumieć, ale w takim razie je wskażcie i dajcie jakieś sensowne wskazówki

Jerzy: Zad 7) Masz sumę dwoch nieskonczonych ciagów geometrycznych: 1/2 + 1/4 + 1/16 + ..... , gdzie a₁ = 1/2 i q = 1/2 1/3 +1/9 + 1/27 ...... , gdzie a₁ = 1/3 i q = 1/3

Nano: Nie wiem za co. Jedyne co nam wykłada to teorię i to też językiem stricte matematycznym. U nas matmę ogarniaja tylko ludzie, którzy się przepisali z innych studiow, a już to mieli

Nano: No i Jerzy mnie naprowadzil − już rozwiązała. Czasami pewnych rzeczy się po prostu nie zauważy. Dziękuję! A co do reszty to jak się zapatrujecie? Dacie jakieś wskazówki do 2 i 5?

ABC: Tak w ogóle to jakie miałaś polecenie do zadania? Tylko zbadać zbieżność czy tam gdzie się da obliczyć też sumę szeregu?

jc: Nano, możecie przecież zadawać pytania. Może wykładowca nie zdaje sobie sprawy, że niewiele rozumiecie. Wiem, że czasem studenci nie kojarzą szeregu z dodawaniem, tylko z kryteriami zbieżności.

Nano: Żadnego. Dał przykłady i tyle. Wcześniej zrobił przykłady gdzie sprawdzał bezwzględną zbieżność, gdzie też mało kto wiedział o co chodzi. Jak poszłam zadac pytania to mi powiedział, żeby" pomyśleć więcej po prostu ". Tak było z moimi poprzednimi zadaniami. On ich nam nie sprawdza, ale nie chce mieć zonka na kolosie

jc:

	n^n+1/n
Tam jest ∑		?
	(n+1/n)ⁿ

n^n+1/n		nⁿ		1
	>		=		≥1/e
(n+1/n)ⁿ		(n+1)ⁿ		(1+1/n)ⁿ

Może można prościej, w każdym razie wyraz ogólny szeregu, czyli

n^n+1/n
	nie jest zbieżny do zera i dlatego szereg jest rozbieżny.
(n+1/n)ⁿ

Nano: A czemu to tak się robi? Jest rozbieżny dlatego, że nie jest równy zero, tak?

Nano: I czemu zamiast n jest potem 1?

Nano: Aaa wiem, bo wyciągnąłes potem n przed nawias

Jerzy:

nⁿ
	= ... dzielisz licznik i mianownik przez nⁿ ... =
(n+1)ⁿ

1

1

1

=

=

=

 n +1 
(
)n
 n 

 1 
(1 + 
)n
 n 

e

Chong: 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Chong: 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jc: 1/2 +1/4+1/8+ ... = 1 nie jest to zerem, a szereg jest zbieżny. Wyraz ogólny szeregu a₁+a₂+a₃+... to ciąg a_n. Jeśli szereg a₁+a₂+a₃+... jest zbiezny to a_n →0. Zatem, jeśli nie a_n nie jest zbieżny do zera, to szereg a₁+a₂+a₃+... jest rozbieżny.

Nano: A wiecie może jak 5 ugryźć? Bo gdyby był to pierwiastek n−tego stopnia to wydaje mi się, że łatwiej by było.trzeba tu jakieś tw Cauchego zastosować?

Nano: Chyba, że źle przykład przepisałam

Nano: Ktoś coś 5?