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???un=nn 2+1 ???un=ch(n)ch(2n)???un=1pn 211pn
2+1 ???un= e1 +1n n ???un= nn+1 n2???un=1ncos2n???un=1(lnn)lnn u n=1n 1+1n e1 +1n nn

3=2 bn3=2c+n?

v n=1n(n+ 1)n X k=1ku k? +1X n=1u n=+1X n=1v X anb n??Xb ???un= en???un=lnnn ???un= exp((lnn)) X n1 ln(n) +aln(n+ 1) +bln(n+ 2)? ap1 +bp2 +cp3 +ap4 +bp5 +cp6 u n=n1 +2n;vn=2n1 +2n;wn=11 +2n? u n=1n Z 1=n 0 f(tn)dt? u

1=nn= 11n

+ o1n ????a >0? u n=a(a+ 1):::(a+n1)n!? ?????? ??? ?? ?????? ?? ?? ????? ?? ????? ??????? un? ?? ???x2R+? ????n2N? ?? ???? u n=n!x nn Y k=1ln 1 +xk ??????? ?? ? ?????? ????? ??????? ln(un+1)ln(un)? ln(un+1)ln(un)ln 1 +1n v n=u2n+u2n+1? Xu

Xmax(un;vn);Xpu

nvn??Xunvnu n+vn? Xpu ? ??????? n2N? ?? ???? v n=un1 +un?

Pun??Pvn???? ?? ???? ???????

v n=unu

1++un?

??????(un)n0??(vn)n0????(R+)N?????? ???

8n2N;vn=11 +n2un?

u n=a0a1:::an?? n X k=1u knun X ?? ?????P+1 k=11k 2=26 +1X k=11k

2(k+ 1)2

???????P+1 +1X n=0n+ 1n!??+1X n=0n 22n!?
+1X n=1x n(1xn)(1xn+1)? S m=+1X n=11n(n+ 1):::(n+m)? ????p2N? ?? ???? a p=+1X n=0n p2 n? ?? ??????? ??? ap2N? ??????2]2;+1[??(an)?? ????? ?????? ??? a

0=??an+1=a2n2???? ????n2N?

+1X n=01a

0a1:::an=12

p 24?
u n+1u nvn+1v n? ??????? ???un=n!+1O(vn)? u n+1u n=n!+11n + o1n ???? >1? u n+1u n=n!+11n + o1n ???? <1?

Pun???????

n= 1n +vn? n nn!en?? u n=13 nn!n Y k=1(3k2)??vn=1n 3=4? ??? ??????? ? ???n????? ?????? u n+1u nvn+1v n? n? v n=un+1S n????Sn=nX k=0u k?

Pun??Pvn??? ???? ???????

?? ????? ????n2N? v n=un=Sn??Sn=u1++un? Pvn? u ?? ???? ?? ????? ???????n R n=+1X k=n+1u k? k=0ak?

8n2N;anS

2n1S n11S n?

Pan=S2n?

?????? ??? ?? ?????? ??Pan=Sn? Xnun? n +1un!0? X n21nlnn? n0apn ???? >1?? ???? () =+1X n=11n Pn k=1pk23 npn???ln(n!)nlnn???Pn k=21klnk ln(lnn) lim a!+1+1X n=1an 2+a2? ????a >0?b >0?? ????n2N? A n=1n n X k=1(a+bk);Bn=nY k=1(a+bk)1=n? ???????limn!+1BnA n P n k=2ln2k X xann 3? X n21n lnn? u n=1n(lnn)? ????2R? ?? ????? ????n2N u n=1P n k=1k? ?????? ?? ?? ????? ?? ????? ???????un? n X k=11k R N=+1X n=N+11n +1X k=01k! +1X k=n+11k!1n:n!? ????(un)?? ????? ?????? ???u02[0;]?? ???? ????n2N? u n+1= 1cosun? ????(un)?? ????? ?????? ???u0>0?? ???? ????n2N? u n+1=p1 +un? ?????? ??? ?? ?????? ?? ?? ????? ?? ????? ???????un`? ??????u02]0;=2[??un+1= sinun???? ????n2N? ??? ??????? un!0+? u n= 1 +12 ++1n

1n+ 1+1n+ 2++1n

2 a n=1n+ 1+1n+ 2++13n? ???? ????n2N? ???? u n=(2n)!(2 nn!)2? lnun+1lnun? ?? ??????? ???un!0? ???? ????n2N? ?? ???? u n=(2n)!(2 nn!)2? ??? ??????? nun!+1? ?? ??????? ?? ?????? ?? ?? ?????Pun? ?? ??????? ?? ?????? ??+1X n=0u nn+ 1? n2N?u n+1u n=n+an+b??????? ??????? un!n!+10? ?? ?????? ???????ln(un)? u nn!+1An ba? (n+ 1)un+1nun=aun+ (1b)un+1 +1X n=0u n? u n+1u n= 1 +n + O1n 2 ;????2R? v n= ln(n+ 1)un+1n un?? ?? ??????? ???? ??????? A2R+???? ?????? u nAn? u

1= 1??un+1= (1 +=n)un?

v n= ln(n+ 1)un+1n un ?? ??????? ???? ??????? A2R+???? ??????unAn? u n=n!enn n+1=2 ????u02]0;2[????

8n2N;un+1= sin(un=2)?

??? ??????? (un)???? ???? ?? ??? ??????? lim(2nun) =A???? ?? ???????A >0? ??????? ?? ?????? ?????n!+1?? n X k=1 kn n u nn!+11n ?? ???? ch(n)en=2?????n???? ????+1?? ???? u nn!+1e ne

2n= en?

u n=2pn

21 +pn

2+ 11pn

21pn

2+ 1n!+11n

3? 1 +1n n = exp nln 1 +1n = e12 en + o1n u nn!+1e2n? ???un= exp(n2ln(1 + 1=n)) = exp(n+ o(n))????n2un!n!+10?? ?? ????? nu n=1n 1=n = exp 1n lnn !1 ???? ????n????? ????? u n12n e 1 +1n n = O1n n

3=2n3=2+n=n+ O(1)n

e1 +1n nn

3=2 bn3=2c+n= O1n

2 N X n=1v n=NX k=1N X n=kku kn(n+ 1) NX n=1v n=NX k=1ku kN X n=k 1n 1n+ 1 =NX k=1N+ 1kN+ 1uk NX n=1v n=NX k=1u kNvN? NX n=1v nNX k=1u k+1X k=1u k nv n=nX k=1u knX k=1v k (nvn)????? ??? ??????`2R[ f+1g? nv n!0 NX k=1u k=NXquotesdbs_dbs14.pdfusesText_20

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