Delermine whether the given sequence Ean 3 converges are diverges w/ an at given In each case prove your conclusions GA LA+ VA
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# Im stuck, I got this wrong on the HE a few days ago, and found the solution but don't know how to do it. The

images are my original work, then the solution from the text book, and finally I rewrote the question. .

Delermine whether the given sequence Ean 3 converges are
diverges w/ an at given In each case prove your conclusions
GA LA+ VA

F3
F4
# 2d ) an antha LE
F10
let 2 70 be given fe
F11
FIVE STAR.
In 4.
let us choose At to be an end/ger wakethe 7 ( 2 - 2)2
Then an = Zatin
n
(E - 2 ) 2
start w / -
2 ( # - 2 ) + 1 2 2 ( 2 - 2) (2 ( 2 - 2 ) + VJ 2 )
Enter
FIVE STAR.
an - z
=
2 ( # - 2 ) - ( # 2 ) 2
* - - 2 well converge to - 2
2 ( - 4 ) + ( 5 .66 )
2
TO
Thus we have proven as converge to 2 Ctrl
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FIVE STAR. | |FIVE STAR.
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60
70
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(c) We prove that lim a, - 0. Let = &gt; 0 be given. We need to find n* EN so that a,, - O ce for all
nant . But, a,
n P
&lt;= if n&gt;
Thus, if n* &gt;
. then a, &lt;= for all n an*.
(d) We prove that Ihn a,, -
_. Let = = 0) be given. We need to find n* E N so that a, -5 2= for all
2
nan. But, a, -
VA
In
2
An + 274
4n
4vn
ceilna
16E
2
Thus, if 1* &gt; -
16-2 . then da - 5
CE .

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