n=1 35. Suppose x is an accumulation point of {a,:n E J}. Show that there is a subsequence of {a,}=1 that converges to x.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Please help me!! The sec pic is my answer but still incomplete. I don’t know how to correct
n=1
35. Suppose x is an accumulation point of {a,:n E J}. Show that there is a subsequence of
{an}=1 that converges to x.
Transcribed Image Text:n=1 35. Suppose x is an accumulation point of {a,:n E J}. Show that there is a subsequence of {an}=1 that converges to x.
you don't date qdues yet
antJbi.there ove
accomulation
elements ot AnkElan nes such that l ank - X|eE
find anz
porut of Pan=n
Infuitly mory.
Stae X is
an
For
Such that l anz - x| c
he
Can
ana t (x-}, *+±)
For {=}, we can find An3 Such that lans- Xl<
ane, Ara,
la ja. Sm be
sequence and
then int al bee any sequence ot poritive
Integers such that
ni ehecn -
of pany
to
a subsequence
an clement Onk q X in/l an= neJY such that
Thus
Ts
For each E E N, thele is
Hir
let Eso, N>
lane
You caumot clsoese
that
...
amete
must
lee determeinmed
Need
to ex plaim this rcsre
portsety
Transcribed Image Text:you don't date qdues yet antJbi.there ove accomulation elements ot AnkElan nes such that l ank - X|eE find anz porut of Pan=n Infuitly mory. Stae X is an For Such that l anz - x| c he Can ana t (x-}, *+±) For {=}, we can find An3 Such that lans- Xl< ane, Ara, la ja. Sm be sequence and then int al bee any sequence ot poritive Integers such that ni ehecn - of pany to a subsequence an clement Onk q X in/l an= neJY such that Thus Ts For each E E N, thele is Hir let Eso, N> lane You caumot clsoese that ... amete must lee determeinmed Need to ex plaim this rcsre portsety
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