qator yaqinlashishining zaruriy sharti

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1576157541.doc { } n a n k1 n а = å å å ¥ = ¥ + = + + + = + + = 1 л 1 n k k 2 n 1 n k n a ... a a а 12 1 limlim(...)lim n nnk nnn k ssaaaa ®¥®¥®¥ = ==+++= å å ¥ = 1 k k q å = + - - = = n k n k n q q q q s 1 1 1 1 q 1 lim n n q + ®¥ =+¥ { } 1 + n q { } n s 1 > q 1 q = 1 - = q å ¥ = 1 k k a å ¥ = + 1 k k n a 1 11111 ...... 122334(1)(1) n nnnn ¥ = +++++= ×××++ å [ ] n , 1 1111111111111 ...... 122334(1)12233411 11 1. 11 n …

an (1) kabi ifodalanadi va umumiy holda kabi belgilanadi. ta’rif: an sonli ketma - ketlikning hadlaridan tuzilgan a1 + a2 +…+ an +…= (2) ifodaga sonli qator deyiladi. sonli qatorning umumiy hadi an dan iborat bo’lib, a1, a2,… lar (2) qatorning hadlari deyiladi. s1=a1; s2=a1+a2; s2=a1+a2+ a3;…; sn=a1+ a2+…+ an (3) larga berilgan (2) qatorning xususiy yig’indilari deyiladi. quyidagi (4) qatorga (2) ning n qoldig’i deyiladi. bunda k – hadi an+1 ga teng. qator yig’indisi deb (2) qatorning n → ∞ dagi limitiga aytiladi va yig’indi (5) kabi ifodalanadi. qatorlar ketma – ketlikning alohida ko’rinishlaridan iborat bo’lganligi sababli, ularning yaqinlashuvchi yoki uzoqlashuvchi ekanligini aniqlash qatorlar nazariyasining asosiy maqsadlaridan biri bo’lib hisoblanadi. agar n ning cheksiz o’sishi bilan (2) qatorning (3) xususiy yig’indilari chekli limitga ega bo’lsa, (2) qatorga – yaqinlashuvchi qator deyiladi. agar xususiy yig’indilari chekli limitga ega bo’lmasa, (2) qatorga – uzoqlashuvchi qator deyiladi. 1-misol. quyidagi qatorning yaqinlashuvchi yoki …

alabalarga havola qilinadi). quyidagi teoremani ham isbotsiz keltiramiz: 2-teorema. agar hadlari manfiy bo’lmagan qatorning xususiy yig’indilari ketma – ketligi chegaralangan bo’lsa, u holda qator yaqinlashadi. agar hadlari manfiy bo’lmagan qatorning xususiy yig’indilari ketma – ketligi chegaralanmagan bo’lsa, u holda qator uzoqlashuvchi bo’ladi. 2-misol. qatorning yaqinlashishini ko’rsating: yechilishi: berilgan qatorning dagi xususiy yig’indisining shaklini o’zgartiramiz, ya’ni: bunda, . demak, berilgan qator chekli limitga ega ekan. mustaqil yechish uchun mashqlar № 1. umumiy had berilgan bo’lsa, uning 5 ta hadini toping: a) b) № 2. qatorning umumiy hadini toping: a) b) v) g) № 3. xususiy yig’indilarini toping va yaqinlashishini tekshiring. yaqinlashuvchi bo’lsa, uning yig’indisini toping. № 4. yaqinlashishini tekshiring. № 5. qatorning yaqinlashishini tekshiring, yaqinlashuvchi bo’lsa, s ni toping: № 6. quyidagi qator yaqinlashuvchimi: 2+22+23+…+2n+…? № 7. qatorni tekshiring: 2. qator yaqinlashishining zaruriy sharti teorema. agar umumiy hadli qator yaqinlashuvchi bo’lsa, u holda n→∞ da =0 bo’lishi zarur. isboti: berilgan qator …

ning zaruriy sharti bajariladimi: ? № 10. ushbu qator uchun yaqinlashishning zaruriy sharti bajariladimi: ? № 11. quyidagi garmonik qator uchun yaqinlashishning zaruriy sharti bajarilishini tekshiring: № 12. qator yaqinlashishining zaruriy sharti bajarilishini tekshiring: _1239646128.unknown _1243704810.unknown _1253358966.unknown _1254831090.unknown _1254833343.unknown _1254833524.unknown _1253359054.unknown _1253359233.unknown _1253359278.unknown _1253358973.unknown _1250494565.unknown _1250494599.unknown _1250494623.unknown _1250494703.unknown _1250494586.unknown _1250494478.unknown _1250494497.unknown _1250494459.unknown _1250494381.unknown _1239646343.unknown _1239647315.unknown _1239648162.unknown _1243445158.unknown _1243445384.unknown _1243445545.unknown _1239648210.unknown _1239648271.unknown _1239647928.unknown _1239648115.unknown _1239647654.unknown _1239646656.unknown _1239646900.unknown _1239646430.unknown _1239646227.unknown _1239646262.unknown _1239646187.unknown _1239640283.unknown _1239645071.unknown _1239645972.unknown _1239646066.unknown _1239645371.unknown _1239640340.unknown _1239643815.unknown _1239640318.unknown _1239639811.unknown _1239640168.unknown _1239640254.unknown _1239640102.unknown _1239639339.unknown _1239639694.unknown _1239598038.unknown

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1576157541.doc { } n a n k1 n а = å å å ¥ = ¥ + = + + + = + + = 1 л 1 n k k 2 n 1 n k n a ... a a а 12 1 limlim(...)lim n nnk nnn k ssaaaa ®¥®¥®¥ = ==+++= å å ¥ = 1 k k q å = + - - = = n k n k n q q q q s 1 1 1 1 q 1 lim n n q + ®¥ =+¥ { } 1 + n q { } n s 1 > q 1 q = 1 - = q å ¥ = 1 k k a å ¥ …

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