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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

noEPk;soh dk rfDs

B'N • ;hwktK T[Zs/ gqaw/: ns/ T[; T[Zs/ nXkfos gqPBK B{z jZb eo ;eDr/.

• cbB dh ;hwk gsk eoB dh ftXh B{z ikD ;eDr/.
• i:kfwsh gfoGkPk B{z ikDB bJh.
• fe;h fpzd{ T[Zs/ cbB dh brkskosk gsk eoB dh ftXh ns/ T[; Bkb ;zpzXs
;wZf;nktK B{z jZb eoB bJh.
• brksko cbBK T[Zs/ gqw/: ns/ T[; T[Zs/ nXkfos gqPBK B{z jZb eoB ftZu n;kBh
j't/rh.
gq;sktBk (Introduction)

1H fBwBfbys i:kfwsh Pq/Dh (Geometrical Series) d/ :'r T[Zs/ ftuko eo'^
1 1 1
+ + + HHHHHHHH nBzs sZe.
2 2 2 2 3
1 gd dk :'rcb & H5
2 gdK dk :'rcb & H75
3 gdK dk :'rcb & H875
4 gdK dk :'rcb & H9375
5 gdK dk :'rcb & H96875
6 gdK dk :'rcb & H984375
7 gdK dk :'rcb & H9921875
8 gdK dk :'rcb & H99609375

9 gdK dk :'rcb & H998046875
10 gdK dk :'rcb & H9990234375
HHHHHHHHHHHHHHHHHHHHHH & HHHHHHHHHHHHHHHHHH
T[Zgo s'A gsk uZbdk j? fe fit/A^fit/A gdK dh ;zfynk tZXdh iKdh j? T[;h soQK Pq/Dh dk :'rcb 1
tZb nZr/ tZXdk j?. Gkt/A :'rcb n;b ftZu 1 d/ pokpo BjhA j' gkT[Adk.
fJ; soQK gdK dh T[fus ;zfynk b? e/ :'rcb ns/ 1 d/ nzso B{z n;hA fizBk ukjhJ/ T[Bk xZN eo
;ed/ jK.
2H wkB fbU fdZsh j'Jh sfoi:k d/ r'b/ d/ nzsors fJZe
;w^pj[G[i pDkfJnk iKdk j?. i:kfwsh s'A ;gPN j? fe
(i) pj[G[i dk y/socb, r'b/ d/ y/socb s'A tZX BjhA j'
;edk, Gkt/A pj[G[i ftZu G[iktK dh ;zfynk fezBh jh tZX feT[A
Bk j't/.

(ii) pj[G[i ftZu G[iktK dh ;zfynk B{z ngfofws o{g s'A
tXkT[D s/ n;hA r'b/ ns/ pj[G[i d/ y/socb d/ nzso B{z
fizBk ukjhJ/ xZN eo ;ed/ jK.

e?be[b; ftZu fJ; sZE B{z fJ; soQK efje/ ftnes ehsk iKdk
j? fe r'b/ d/ nzsors fyZu/ rJ/ pj[G[i d/ y/socb dh ;hwk, id'Afe G[iktK dh ;zfynk ngfofws
o{g Bkb tZXdh j? (iK nBzs tZb gqtfos j[zdh j?), r'b/ dk y/socb j[zdh j?.
lim (pj[G[i dk y/socb) & r'b/ dk y/socb.
n→∞

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