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my professor says I have to explain the steps in the solved problems in the picture. Not just copy eveything down from the text.

my professor says I have to explain the steps in the solved problems in the picture. Not just copy eveything down from the text.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 74E
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2.20) my professor says I have to explain the steps in the solved problems in the picture. Not just copy eveything down from the text.
Least upper bound, greatest lower bound, limit superior, limit inferior 2.20. Find the (a) L.u.b., (b) g.l.b., (c) lim sup ( lim ), and (d) lim inf (lim) for the sequence 2, -2, 1,-1, 1, –1, 1, -1,.... (a) 1.u.b. = 2, since all terms are less than equal to 2, while at least one term (the 1st) is greater than 2 – e for any e > 0. (b) g.l.b. = -2, since all terms are greater than or equal to -2, while at least one term (the 2nd) is less than -2 + e for any e > 0. (c) lim sup or lim = 1, since infinitely many terms of the sequence are greater than 1 - e for any e > 0 (namely, all l's in the sequence), while only a finite number of terms are greater than 1 + e for any e >0 (namely, the 1st term). (d) lim inf or lim =-1, since infinitely many terms of the sequence are less than –1 + e for any e > 0 (namely, all –l's in the sequence), while only a finite number of terms are less than -1 - e for any e > 0 (namely, the 2nd term).
Transcribed Image Text:Least upper bound, greatest lower bound, limit superior, limit inferior 2.20. Find the (a) L.u.b., (b) g.l.b., (c) lim sup ( lim ), and (d) lim inf (lim) for the sequence 2, -2, 1,-1, 1, –1, 1, -1,.... (a) 1.u.b. = 2, since all terms are less than equal to 2, while at least one term (the 1st) is greater than 2 – e for any e > 0. (b) g.l.b. = -2, since all terms are greater than or equal to -2, while at least one term (the 2nd) is less than -2 + e for any e > 0. (c) lim sup or lim = 1, since infinitely many terms of the sequence are greater than 1 - e for any e > 0 (namely, all l's in the sequence), while only a finite number of terms are greater than 1 + e for any e >0 (namely, the 1st term). (d) lim inf or lim =-1, since infinitely many terms of the sequence are less than –1 + e for any e > 0 (namely, all –l's in the sequence), while only a finite number of terms are less than -1 - e for any e > 0 (namely, the 2nd term).
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