sn ) ≤ lim m→∞ ( inf n>m tn ) = lim inf tn A similar proof works for lim sup Problem 7 (12 2) Prove that lim supsn = 0 if and only if lim sn = 0 Solution If lim
| Previous PDF | Next PDF |
[PDF] Math 3150 Fall 2015 HW2 Solutions
(b) Show that if L > 1, then limsn = +∞ Solution (a) Define the sequence rn = \ \ \ sn+1
[PDF] Homework 4 Solutions
(c) Prove that if limsn and limtn exist, then limsn ≤ limtn Solution (a) Let M > 0 Since sn → +∞ (b) Show that if L > 1, then limsn = +∞ Hint: Apply (a) to the
[PDF] HOMEWORK 5 - UCLA Math
sn ) ≤ lim m→∞ ( inf n>m tn ) = lim inf tn A similar proof works for lim sup Problem 7 (12 2) Prove that lim supsn = 0 if and only if lim sn = 0 Solution If lim
[PDF] 4 Sequences 41 Convergent sequences • A sequence (s n
If (sn) converges to s then we say that s is the limit of (sn) and write s = limn sn, or Proof (a) (⇐) If (sn) is a sequence in S with limit x, and if ϵ > 0 is given, then
[PDF] Problem Sheet 6 1) a) Show that if lim sn = ∞, then lim 1 sn = 0 b
a) a problem from the previous sheet b) the Squeeze Theorem 4) Prove that if sn ≤ tn for all n and lim n→∞ sn = ∞, then lim n→∞ tn = ∞ 5) Use the Squeeze
[PDF] Math 104: Introduction to Analysis SOLUTIONS Alexander Givental
Let a, b ∈ R Show that if a ≤ b+ 1 Assume all sn = 0 and that the limit L = lim sn+1/sn exists Prove that (sn) is bounded if and only if lim sup sn < +∞
[PDF] Homework 3
lim bn = s Prove lim sn = s This is called the “squeeze lemma ” (b) Suppose (sn) and (tn) are (a) Show that if sn ≥ a for all but finitely many n, then lim sn ≥ a
[PDF] Homework 6
Section 12 12 2 Prove limsup sn = 0 if and only if lim sn = 0 12 4 Show limsup( sn + tn) ≤ lim sup sn + lim sup tn for bounded sequences (sn) and (tn) Hint
[PDF] Solutions for Homework Math 451(Section 3, Fall 2014)
8 4) Claim: If (tn) is a bounded sequence and (sn) is a sequence such that limsn = 0, then (Alternatively, we could simply prove directly that lim−tn = 0 ) Then
[PDF] Limits
These examples should suggest a result: Theorem 2 20 Let (sn) be a sequence Then lim inf sn = lim sup sn if and only if lim sn = s for
[PDF] show that p ↔ q and p ∧ q ∨ p ∧ q are logically equivalent
[PDF] show that p(4 2) is equidistant
[PDF] show that p2 will leave a remainder 1
[PDF] show that the class of context free languages is closed under the regular operations
[PDF] show that the class of turing recognizable languages is closed under star
[PDF] show that the family of context free languages is not closed under difference
[PDF] show that the language l an n is a multiple of three but not a multiple of 5 is regular
[PDF] show that x is a cauchy sequence
[PDF] show that x is a discrete random variable
[PDF] show that x is a markov chain
[PDF] show that x is a random variable
[PDF] show that [0
[PDF] show the mechanism of acid hydrolysis of ester
[PDF] show time zone cisco