{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Cheat Sheat 2

Cheat Sheat 2 - limSn= ∞(a Counterexample An=n^2 Bn=-4n(b...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Theorem : If (Sn) is an unbounded increasing sequence, then limSn=+ . : Let (Sn) be an increasing sequence and suppose that the set S={Sn:n€N} is unbounded. Since (Sn) is increasing, S is bounded below by S1. Hence S must be unbounded above. Thus, given and M€R, there exists an integer N such that SN>M, so
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: limSn=+ ∞ . (a) Counterexample An=n^2, Bn= -4n (b) Counterexample An=n-5, Bn=5n 2.36 Remark Since Sn is bounded by the completeness axiom s=sup{Sn,n € N}=:S exists, such that Sn <= s for all n. Let eps>0 then Sn <= s +eps. By thm 2.9 |Sn-s|<eps. So limSn=sup(Sn). Simular for infSn....
View Full Document

{[ snackBarMessage ]}

Page1 / 2

Cheat Sheat 2 - limSn= ∞(a Counterexample An=n^2 Bn=-4n(b...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon bookmark
Ask a homework question - tutors are online