Announcements : • Quiz 3 today : 7.2 Part 2 7.3 7.4 ,
Midterm Exam o n Monday, June 14th : Ch 5,6 , and 7 . ftsequees
7.6 .7 7
•
Alternating
.
.
–
– t,-it,-,-7→typicallyweLaneC-Din the
.,,
Series lie
⇒ {¥ tzi +Izz) – ¥33s + £44> – ¥s –
– – – – 3 h=1 n=Z n=3 h=4 n=5 n=6j- —
11
11
,
“”””
–
s
an=t§,=(-§)mforn
=
=’ nai f- ”
–
t;I ¥1)
“+5
–
”
” ”
formula
2
ni.=n.It
=
converges .
if✗ =/
–
.¥,-.-.}
={I ¥
1in :÷÷ In 1-
→☐ ,,,
>
I ⇒ {I¥, } me/dee? ftx)= ⇒ f-“✗1–4×31×4 4×3>
=μ =¥×÷so
“”
increasing – z An <⇒
( "
Cntiittl
3 T¥ ⇐ ,
is n'[4+15+1] 2h4 former
Boot
,
(n+D"(n'41)
⇒
Ant
<⇒ ⇒ Is 1¥, El fornal ⇒ bold.
(n+
,
)4
3 {0¥} na
Cosx
oscillates
btwn -13 1 ⇒ -1<-65×2-1 . not monotonic .
⇒ co¥ is
[⇒ IrnIco÷±¥ for
1in
nix
↳
nai
Squeeze
⇒
-tn=o & long ¥ = o . By
Thinning co÷=o
converges .
co÷
is bad
for v21
.
In-1) (n -
÷.
Y
-----
2) 3zI
Observe:
n! In"
C- 1) ! ⇒ meaningless . =±
Proo¥
tg- E- Z- ¥= %± In=t4
Since
t.mn#n--- 0
Tu m lm ,⇒
n =
.
f
±
's- ⇒
-
AID ALI n h=2- :
,
converges
.
by
squeeze
n⇒h÷=0 =
-.
=-3
:
§. 2-3-F-=F-£ =§
:
f- In
=/
n=4_ : o±n÷±tn
I-
Zz = I E tu = I ,
I
5.4.3- 2- I ⇒ b-terms 6- 2-⇒
FEELS :
7 ! 7- 5. 4- 3- I 7- terms
9'I &re