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VED1
E L-LOVELY-H math2-1 IInd 21-10-11 IIIrd 24-1-12 IVth 21-4-12 Vth 20-8-12 VIth 10-9-12

fJekJh^2 L ;hwk ns/ brkskosk

3H eqw dh ;hwk (Limit of a Sequence)^eqw B'N

111 1
1, , , , ,........
2345
1
T[Zs/ ftuko eo' fi;d/ bJh s = , fiZE/ s eqw dk n tK gd gqdofPs eodk j?. n;hA d/yd/ jK
n
n
n
1
fe n dk wkB fit/A^fit/A tZXdk j? dk wkB T[t/A^T[t/A xNdk j?. n;b ftZu n;hA n B{z T[fus
n
1 1
tZv u[D e/, B{z fizBk ukjhJ/ T[Bk S'Nk eo ;ed/ jK. fJZE/ i/eo n >10,000 sK <0.0001
n n
-8
8
ns/ i/eo n >10 sK 1 <10 fJ; soQK n;hA d/yd/ jK fe fit/A^fit/A n nBzs d/ tZb gqtfos
n
1
j[zdk j? Iho' d/ tZb gqtfos (tends to) j[zdk j?. n;hA d/yd/ jK fe eqw {s n } dh ;hwk 0 j? ns/
n
fJ; B{z lim s n & 0 d[nkok fbnk iKdk j?.
n→∞
1 234
j[D n;hA d{i/ eqw 0, , , , ,........
234 5
n − 1
T[Zs/ ftuko eoKr/ fi;d/ bJh s = n;hA d/yd/ jK fe fit/A^fit/A n tZXdk j? s T[t/A^T[t/A 1
n
n
n
d/ B/V/ gj[zudk j?. d{i/ PpdK ftZu n B{z T[fus tZvk u[D e/ n;hA s ns/ 1 d/ nzeVk nzso Gkt
n
s − 1 B{z fizBk S'Nk ukjhJ/, eo ;ed/ jK. fJ; eqw d/ bJh
n
lim s n & 1
n→∞
;XkoD s"o s/ fe;h eqw s 1 , s 2 , s 3 ,........ d/ bJh n B{z T[fus tZvk u[DB s/ i/eo s ns/ fe;h
n
;zfynk A d/ nzeVk nzso s − A B{z n;hA fizBk ukjhJ/ T[Bk fJZSk nB[;ko S'Nk eo ;ehJ/ A B{z
n
eqw {s n } dh ;hwk efjzd/ jB ns/ fJ;B{z
lim s n & A
n→∞
d/ d[nkok fbfynk iKdk j?.
j[D eqw
2
2
2
2
2
1 , 2 , 3 , 4 , HHHHHHHHHHHHH n ,HHHHHHHHHHHH
T[Zs/ ftuko eoB s/ n;hA d/yd/ jK fe fit/A^fit/A n dk wkB tZXdk j?, s th T[t/A^T[t/A tZXdk iKdk
n
j?. n;hA n B{z T[fus tZvk b? e/ s B{z fizBk tZvk ukjhJ/, eo ;ed/ jK. fJZE/ s >10,000 i/eo
n
n
8
4
n>100, s n > 10 i/eo n > 10 , n;b ftZu fJZE/ s n B{z fe;h th tZvh s'A tZvh ;zfynk s'A th tZvk
pDkfJnk ik ;edk j?. fJ;B{z n;hA S →∞ , i/eo n →∞ d/ d[nkok ftnes eod/ jK.
n
4H cbB dh ;hwk B{z gfoGkfPs eoB s'A gfjbK n;hA fBwB T[dkjoD T[Zs/ ftuko eoBk T[fus
;wMd/ jK. e[ZM cbB x d/ ftP/P wkB d/ bJh ngfoGkfPs j[zd/ jB fit/A
x − 1
2
() = H
fx
x − 1
x − 1 0
2
;gPN j? fe cbB dk wkB x = 1 T[Zs/ Gkt nfBoXko (indeterminate) j?.
x − 1 0

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