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Файл:Сходимость числовых рядов в примерах и задачах. Учебное пособие
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uf «
u
n
n
f
³
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n
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f
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ɚ
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n
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n
n
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f
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ɩɨɢɧɬɟɝɪɚɥɶɧɨɦɭɩɪɢɡɧɚɤɭɄɨɲɢɦɨɠɧɨɥɢɛɨ
Nn
ɧɚɨɫɧɨɜɚɧɢɢɫɜɨɣɫɬɜɚɱɢɫɥɨɜɵɯɪɹɞɨɜɢɫɫɥɟɞɨɜɚɬɶɫɯɨɞɢɦɨɫɬɶɪɹɞɚ
¦
f
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x
f
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f
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n
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ɦɨɧɨɬɨɧɧɨ ɭɛɵɜɚɸɳɟɣ ɧɚ ɩɪɨɦɟɠɭɬɤɟ
unf «
n
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f
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u
n
nn
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n
f
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ɬɚɤ ɱɬɨ
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f
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ɊɟɲɟɧɢɟɊɚɫɫɦɨɬɪɢɦɮɭɧɤɰɢɸ
ɭɛɵɜɚɟɬɧɚɩɪɨɦɟɠɭɬɤɟ
ɬɟɝɪɚɥȿɫɥɢ z
f
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p
n
n
xf
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p
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p
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p
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f
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n
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ɫɯɨɞɢɬɫɹɩɪɢ
Ɉɬɜɟɬɫɯɨɞɢɬɫɹɩɪɢ !
f
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n
n
ɢɪɚɫɯɨɞɢɬɫɹɩɪɢ dp
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f
ɉɪɢɦɟɪɂɫɫɥɟɞɨɜɚɬɶɫɯɨɞɢɦɨɫɬɶɪɹɞɚ
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n
n
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f
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n
nn
n
Ɂɧɚɱɢɬɨɧɪɚɫɯɨɞɢɬɫɹɤɚɤɨɛɨɛɳɟɧɧɵɣɝɚɪɦɨɧɢɱɟɫɤɢɣɪɹɞɫɩɨɤɚɡɚɬɟɥɟɦ
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n
ɗɬɚɮɭɧɤɰɢɹɩɨɥɨɠɢɬɟɥɶɧɚɢ
ɭɛɵɜɚɟɬɧɚ ɩɪɨɦɟɠɭɬɤɟ
> f ɂɫɩɨɥɶɡɭɹ ɢɧɬɟɝɪɚɥɶɧɵɣ ɩɪɢɡɧɚɤɄɨɲɢ ɜɵɱɢɫ
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f
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b
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n
n
n
e
Ɉɬɜɟɬɪɹɞɫɯɨɞɢɬɫɹ
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n
ɊɟɲɟɧɢɟȾɥɹ ɢɫɫɥɟɞɨɜɚɧɢɹ ɞɚɧɧɨɝɨɪɹɞɚɛɭɞɟɦɢɫɩɨɥɶɡɨɜɚɬɶɢɧɬɟɝɪɚɥɶ
ɧɵɣ ɩɪɢɡɧɚɤ ɄɨɲɢȾɥɹ ɷɬɨɝɨɪɚɫɫɦɨɬɪɢɦ ɮɭɧɤɰɢɸ
xfOQ ɢɩɪɨɜɟɪɢɦ
x
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ɮɭɧɤɰɢɹ
ɮɭɧɤɰɢɹ
xfOQ ɩɨɥɨɠɢɬɟɥɶɧɚɩɪɢ
xfOQ ɦɨɧɨɬɨɧɧɨɭɛɵɜɚɟɬ ɩɪɢ
x
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!
t
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c
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xf
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ɰɢɹ
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t
ɢ ɩɨ ɫɜɨɣ
ɫɬɜɭɱɢɫɥɨɜɵɯɪɹɞɨɜɩɟɪɜɵɟɱɥɟɧɨɜɪɹɞɚɧɟɦɟɧɹɸɬɫɯɨɞɢɦɨɫɬɢɪɚɫɯɨɞɢɦɨɫɬɢ
ɞɚɧɧɨɝɨ ɪɹɞɚ ɬɨ ɩɪɢɦɟɧɢɦ ɢɧɬɟɝɪɚɥɶɧɵɣ ɩɪɢɡɧɚɤ ɫɯɨɞɢɦɨɫɬɢ ɤ ɢɫɫɥɟɞɨɜɚɧɢɸ
f
n
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n
OQ
Ⱦɥɹɷɬɨɝɨɜɵɱɢɫɥɢɦɧɟɫɨɛɫɬɜɟɧɧɵɣɢɧɬɟɝɪɚɥ
n
f b
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dx
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fo
b
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x
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dx
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ɪɹɞɚ
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