Page 41 - DECO403_MATHEMATICS_FOR_ECONOMISTS_HINDI

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

bdkbZ lhek o lrrrk

oSQyoqQyl esa bl rF; dks bl izdkj dgdj O;Dr fd;k tkrk gS fd o`Ùk osQ vUrxZr [khaps x;s cgqHkqt osQ uksV
{ks=kiQy dh lhek] tcfd Hkqtkvksa dh la[;k vifjfer :i ls c<+rh gS (vFkok vuUr dh vksj izo`Ùk gksrh gS)]
o`Ùk dk {ks=kiQy gksrh gSA

lim (cgqHkqt dk {ks=kiQy) : o`Ùk dk {ks=kiQyA
n→∞
3- vuqØe dh lhek 3 , 0 @
µvuqØe

9 11 1 1
, ,......
, ,
2 345
1
ij fopkj dhft, ftlosQ fy, : ] tgk¡ vuqØe dk #ok¡ in iznf'kZr djrk gSA ge ns[krs gSa fd #

n
1 1
dk eku tSls&tSls c<+rk gS dk eku oSls&oSls ?kVrk tkrk gSA okLro esa ge # dks i;kZIr cM+k pqudj]
n n
1

dks ftruk pkgsa mruk NksVk dj ldrs gSaA ;gk¡ ;fn # K -9--- rks L - --- vkSj ;fn # K - rks
n
1 1
n
n L - bl izdkj ge ns[krs gSa fd tSls&tSls # vuar dh vksj izo`Ùk gksrk gS 'kwU; dh vksj izo`Ùk

gksrk gSA ge ns[krs gSa fd vuqØe D E dh lhek - gS vkSj bls lim s : -
n

n→∞
}kjk fy;k tkrk gSA
12 34
vc ge nwljs vuqØe -9 , , , ,......
23 4 5
n − 1
ij fopkj djsaxs ftlosQ fy, n ge ns[krs gSa fd tSls&tSls # c<+rk gS oSls&oSls osQ lfUudV igq¡prk

gSA nwljs 'kCnksa esa # dks i;kZIr cM+k pqudj ge vkSj osQ lkaf[;d vUrj vFkkZr~ P 8 P dks ftruk NksVk pkgsa]

dj ldrs gSaA bl vuqØe osQ fy,
lim s :
n
n→∞
lk/kj.kr;k fdlh vuqØe 9 9 9 osQ fy, # dks i;kZIr cM+k pquus ij ;fn vkSj fdlh la[;k

osQ lkaf[;d vUrj P P dks ge ftruk pkgsa mruk bPNkuqlkj NksVk dj losaQ dks vuqØe D E dh lhek

dgrs gSa vkSj bls
lim s :
n
n→∞
osQ }kj fy[kk tkrk gSA
vc vuqØe

9 9 9 9 # 9

ij fopkj djus ij ge ns[krs gSa fd tSls&tSls # dk eku c<+rk gS] Hkh oSls&oSls c<+rk tkrk gSA ge # dks

i;kZIr cM+k ysdj dks ftruk cM+k pkgsa] dj ldrs gSaA ;gk¡ ij K -9--- ;fn # K --9 K - ;fn

# K - ] okLro esa ;gk¡ dks fdlh Hkh cM+h ls cM+h la[;k ls Hkh cM+k cuk;k tk ldrk gSA bls ge

→ ∞] ;fn # → ∞ osQ }kjk O;Dr djrs gSaA