Page 20 - 미적분1 테스트

_ ޷੸࠙ ױਗ QT 1. ಕ੉૑ ."$
ࠗ࠙೤ਵ۽ ੉ܖয૓ ࣻৌ S¡, S™, S£, y, S«, y੉ ੌ੿ೠ ч Sী ࣻ۴ೡ
n ¶
ٸ ૊ lim S«= lim ;K+! a˚=S੉ݶ әࣻ ;N+! a«਷ Sী ࣻ۴ೠ׮Ҋ ೠ׮
n ڦ n ڦ
੉ٸ Sܳ әࣻ੄ ೤੉ۄ ೞҊ ӝഐ۽
ࣻৌ {a«}੄ ࣻ۴ ߊ࢑਷ ¶
lim a«ਸ ઑࢎೞח Ѫ੉Ҋ a¡+a™+a£+y+a«+y=S ژח ;N+! a«=S
n ڦ
әࣻ੄ ࣻ۴ ߊ࢑਷ ৬ э੉ աఋմ׮
lim S«ਸ ઑࢎೞח Ѫ੉׮
n ڦ
¶
ೠಞ әࣻ ;N+! a«੄ ࠗ࠙೤ਵ۽ ੉ܖয૓ ࣻৌ {S«}੉ ߊ࢑ೡ ٸ ੉ әࣻח
ߊ࢑ೠ׮Ҋ ೠ׮ ੉ ҃਋ী Ӓ ೤਷ ࢤпೞ૑ ঋח׮

әࣻ੄ ೤ ҳೞӝ

011
৘ઁ ׮਺ әࣻ੄ ࣻ۴ ߊ࢑ਸ ઑࢎೞҊ ࣻ۴ೞݶ Ӓ ೤ਸ ҳೞৈۄ
¶ 1 ¶ 1
̻ ̼ ;N+! ;N+!
n(n+1) 'ßn+1+'ßn

ಽ੉ әࣻ੄ ઁn೦ө૑੄ ࠗ࠙೤ਸ S«੉ۄҊ ೞݶ
1 1 1
̻ = - ੉޲۽
n(n+1) n n+1
1 1 1 1 1 1 1 1
S«={1- }+{ - }+{ - }+y+{ - }=1-
2 2 3 3 4 n n+1 n+1
1
̻ lim S«= lim {1- }=1
n ڦ n ڦ n+1
ٮۄࢲ ઱য૓ әࣻח ࣻ۴ೞҊ Ӓ ೤਷ 1੉׮
1
̼ ='ßn+1-'ßn੉޲۽
'ßn+1+'ßn
S«=('2-1)+('3-'2)+('4-'3)+y+('ßn+1-'ßn)='ßn+1-1
lim S«= lim ('ßn+1-1)=¶
n ڦ n ڦ
ٮۄࢲ ઱য૓ әࣻח ߊ࢑ೠ׮
̻ࣻ۴ 1 ̼ߊ࢑

01
]ޙઁ] ׮਺ әࣻ੄ ࣻ۴ ߊ࢑ਸ ઑࢎೞҊ ࣻ۴ೞݶ Ӓ ೤ਸ ҳೞৈۄ
¶ 1 ¶ 1
̻ ̼ ;N+! ;N+!
(2n-1)(2n+1) 'ß2n+1+'ß2n-1

28 I. ࣻৌ੄ ӓೠ