2.3.1 adv. calc

2.3.1 adv. calc - en an-= 0 an = < . an ) e f) > Let...

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Nathan Fitzenreider 2.3.1 ( Suppose a ) . n is a sequence of positive real numbers a) ( If a ) → , n 0 t h ( ) → . en an 0 b) ( If a ) → , n x t h ( ) → . en an x c) Proof. a) Because a → , n 0 we know t h at t h ere exists an N N so t h at ⎪an - < 0⎪ ε b) w h ≥ . enever n N Since t h e sequence is positive we can say t h at c) ⎪a n - = 0⎪ ⎪ an⎪ = . an Now c h oose N1 N so t h at d) ⎪a n - < 0⎪ ε 2 a < n ε 2 a < . n ε T h
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Unformatted text preview: en an-= 0 an = < . an ) e f) > Let 0 and a . n x C h oose N N so t h at an-x < x w h . enever n N g) We can rewrite a n-x- + as an x x an . T h is implies t h , at h) a n-x = an-x + x an an-x < . x T h . us an x i) j) k)...
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This note was uploaded on 11/04/2010 for the course MTH MTH 421 taught by Professor Ponds during the Spring '10 term at N. Central IL.

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