Hint: Consider xn = (xn + Yn) — Yn. - Let (xn) and (yn) be bounded sequences in R. Show that lim inf (x + yn) ≤ lim inf x + lim sup yn. 818 818 N→X
Hint: Consider xn = (xn + Yn) — Yn. - Let (xn) and (yn) be bounded sequences in R. Show that lim inf (x + yn) ≤ lim inf x + lim sup yn. 818 818 N→X
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.5: The Binomial Theorem
Problem 21E
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please help proof this and be specific so i can undersatnd. also please include the theorem that you are using to solve this too please
![Hint: Consider xn = (xn + Yn) — Yn.
-](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb20beb72-840b-470a-857a-f2b487ca02a4%2F6960a98c-388b-4a13-97c1-97050d92f7ac%2Fdak6v4l_processed.png&w=3840&q=75)
Transcribed Image Text:Hint: Consider xn = (xn + Yn) — Yn.
-
![Let (xn) and (yn) be bounded sequences in R. Show that
lim inf (x + yn) ≤ lim inf x + lim sup yn.
818
818
N→X](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb20beb72-840b-470a-857a-f2b487ca02a4%2F6960a98c-388b-4a13-97c1-97050d92f7ac%2Fkjcc1a_processed.png&w=3840&q=75)
Transcribed Image Text:Let (xn) and (yn) be bounded sequences in R. Show that
lim inf (x + yn) ≤ lim inf x + lim sup yn.
818
818
N→X
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