qator yaqinlashishining yetarli sharti

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1576320491.doc å ¥ = 1 n n a å ¥ = 1 n n b å ¥ = 1 n n a å ¥ = 1 n n a å ¥ = 1 n n b å ¥ = 1 k k b å ¥ = n k k b b b n k k = å ¥ = å å å = ¥ = = = £ £ n n k n k k k n n k k b b b a å ¥ = n k k a å ¥ = n k k a å ¥ = 1 k k a å ¥ = 1 2 2 sin n n nx , 1 sin 0 2 2 2 булса n n nx £ £ å ¥ = 1 2 1 n n 2 1 n 2 1 n å ¥ = 1 n n a 1 …

or bo`lganligi sababli u uzoqlashuvchidir. 2-misol. qatorni dalamber alomati yordamida tekshiring. yechilishi: berilganlarga ko`ra , bundan u holda, . demak, berilgan qator yaqinlashuvchi ekan. 3–misol. qatorni tekshiring yechilishi: shartga asosan . u holda, . dalamber alomatiga asosan berilgan qator yaqinlashuvchi bo`ladi. 3. koshi alomati qatorning yaqinlashuvchi bo`lishi uchun har qanday son uchun shunday n nomer mavjud bo`lib, barcha n>n lar va p≥1 da tengsizlikning bajarilishi zarur va yetarlidir. qatorning bunday shartiga koshi alomati yoki koshi kriteriyasi deyiladi. bunda p=1 da qatorning yaqinlashuvchi bo`lishi uchun shartning bajarilishi zaruriydir. bu esa ni anglatadi. demak, qatorning yaqinlashuvchi bo`lishi uchun uning nomeri cheksiz oshishi bilan qatorning umumiy hadi nolga intilishi zarur. ammo bu shart qatorning yaqinlashuvchi bo`lishi uchun yetarli bo`la olmaydi. bo`nga quyidagi garmonik qator misol bo`la oladi: bunda n→∞ da bo`ladi, lekin garmonik qator koshi alomatini qanoatlantirmaydi. shuning uchun u yaqinlashuvchi bo`la olmaydi, chunki bundan ko`rinadaki, o da qatorni tekshiramiz. deb olib, berilgan …

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1576320491.doc å ¥ = 1 n n a å ¥ = 1 n n b å ¥ = 1 n n a å ¥ = 1 n n a å ¥ = 1 n n b å ¥ = 1 k k b å ¥ = n k k b b b n k k = å ¥ = å å å = ¥ = = = £ £ n n k n k k k n n k k b b b a å ¥ = n k k a å ¥ = n k k a å ¥ = 1 k k a å ¥ = 1 2 2 sin n n nx , 1 sin 0 2 …

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