# Seq_hnd - Sequences Theorems on Sequences I Modeling...

• Notes
• nizhes
• 1

This preview shows page 1. Sign up to view the full content.

Sequences Theorems on Sequences: I. Modeling Theorem Let { } a n be a sequence, let f n a n ( ) = , and suppose that f x ( ) exists for every real number x 1. (i) lim ( ) x f x L →∞ = , then lim ( ) n f n L →∞ = . (ii) lim ( ) x f x →∞ = ∞ - ∞ (or ) , then lim ( ) n f n →∞ = ∞ - ∞ (or ) . II. Let r be a real number. Then (i) lim n n r →∞ = 0 if r < 1 (ii) lim n n r →∞ = ∞ if r 1 III. Sandwich Theorem If { } a n , { } b n , and { } c n are sequences and a b c n n n for every n and if lim lim n n n n a L c →∞ →∞ = = , then lim n n b L →∞ = . IV. Let { } a n be a sequence. If lim n n a →∞ = 0 , then lim n n a →∞ = 0 V. Suppose that lim n n a →∞ and lim
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: n n b →∞ both exist and are finite. Then (i) lim lim n n n n ca c a →∞ →∞ = for any real number c (ii) lim( ) lim lim n n n n n n n a b a b →∞ →∞ →∞ + = + (iii) ( 29 ( 29 lim lim lim n n n n n n n a b a b →∞ →∞ →∞ = (iv) If lim n n b →∞ ≠ , then lim lim lim n n n n n n n a b a b →∞ →∞ →∞ = . VI. A bounded, monotonic (nondecreasing or nonincreasing) sequence has a limit....
View Full Document

• Spring '08
• varies
• Calculus, Limit, lim, Limit of a sequence

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern