section7and8notes

section7and8notes - Lectures 7 and 8 • Definition of a...

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

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Lectures 7 and 8 • Definition of a sequence, sequence notation, and examples. √ 1 Ex: an = n2 , bn = (−1)n , xn = n. • Informal and formal definitions of the sequence (xn ) converging to x. • Negation of the sequence (xn ) converging to x. • Prove 1 n2 → 0. • Prove (−1)n does not converge to any real number x. • Prove that limits are unique, i.e. if xn → x and xn → y , then x = y . • Prove n2 +2n n3 −5 → 0. • Suppose that each sn > 1 and sn → s. Prove 1 √ sn → √ s. ...
View Full Document

Ask a homework question - tutors are online