Question

Suppose that an is a sequence and lim sup an =a=lim inf an for some a...

Suppose that an is a sequence and lim sup an =a=lim inf an for some a in Real numbers.

Prove that an converges to a

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
let xn be a sequence in R do lim sup xn and lim inf xn always...
let xn be a sequence in R do lim sup xn and lim inf xn always exist R # and why
Prove that if (xn) is a sequence of real numbers, then lim sup|xn| = 0 as...
Prove that if (xn) is a sequence of real numbers, then lim sup|xn| = 0 as n approaches infinity. if and only if the limit of (xN) exists and xn approaches 0.
Show that lim sup n→∞ (−xn) = −(lim inf n→∞ (xn).
Show that lim sup n→∞ (−xn) = −(lim inf n→∞ (xn).
Prove that if E ⊂ R is bounded and sup E ∈ E or inf E...
Prove that if E ⊂ R is bounded and sup E ∈ E or inf E ∈ E, then E is not open. Analysis question (R refers to the real numbers).
Suppose {xn} is a sequence of real numbers that converges to +infinity, and suppose that {bn}...
Suppose {xn} is a sequence of real numbers that converges to +infinity, and suppose that {bn} is a sequence of real numbers that converges. Prove that {xn+bn} converges to +infinity.
prove if lim?→∞ an = a>0 and if lim?→∞ sup bn = b (bn≥0) then lim?→∞...
prove if lim?→∞ an = a>0 and if lim?→∞ sup bn = b (bn≥0) then lim?→∞ sup anbn =ab 0<R<∞ : an∈R
Suppose that f(a) =f(b) and inf {f(x) :x∈[a, b]}< α <sup{f(x) :x∈[a, b]}.Prove that there exist...
Suppose that f(a) =f(b) and inf {f(x) :x∈[a, b]}< α <sup{f(x) :x∈[a, b]}.Prove that there exist c, d∈[a, b] with (c Not equal d) such that f(c) =α=f(d)
Suppose S and T are nonempty sets of real numbers such that for each x ∈...
Suppose S and T are nonempty sets of real numbers such that for each x ∈ s and y ∈ T we have x<y. a) Prove that sup S and int T exist b) Let M = sup S and N= inf T. Prove that M<=N
Prove: If x is a sequence of real numbers that converges to L, then any subsequence...
Prove: If x is a sequence of real numbers that converges to L, then any subsequence of x converges to L.
Using the definition of convergence of a sequence, prove that the sequence converges to the proposed...
Using the definition of convergence of a sequence, prove that the sequence converges to the proposed limit. lim (as n goes to infinity) 1/(n^2) = 0