21- §. Limit.
(an) ketma-ketlik uchun shunday N natural son topiladiki, bunda n>N shart hamda shart o’rinli bo’lsa, (an) ketma-ketlikning chegarasi a deyiladi( bunda juda kichik bo’lgan musbat sondir). Bu yuqoridagi ifodaning ko’rinishini quyidagicha yoziladi.
yoki n bo’lganda an bo’ladi.
Quyidagi teoremalarni eslab qoling.
1)Agar ketma-ketlik yaqinlashuvchi bo’lsa, u faqat bitta chegaraga ega bo’ladi.
2)agar ketma-ketlik yaqinlashuvchi bo’lsa, u chegaralangan
3)agar an va bn ketma-ketliklar yaqinlashuvchi quyidagi tasdiqlar doimo o’rinlidir.
a)
b)
c)
d) (bunda bn va )
e)![](data:image/png;base64,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)
Quyidagi ajoyib limitlarni eslab qoling.
1) =1 2)
3) 4) 5)
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