Question

If {sn} is a sequence of positive numbers converging to a positive number L, show that...

If {sn} is a sequence of positive numbers converging to a positive number L, show that √ {sn} converges to √ L.

Do not solve using calc but rather an N epsilon proff

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
Telescoping Series. Let {an} ∞ n=0 be a sequence of real numbers converging to zero, limn→∞...
Telescoping Series. Let {an} ∞ n=0 be a sequence of real numbers converging to zero, limn→∞ an = 0. Let bn = an − an+1. Then the series X∞ n=0 bn converges.
Show that sequence {sn} converges if it is monotone and has a convergent subsequence.
Show that sequence {sn} converges if it is monotone and has a convergent subsequence.
Suppose (an), a sequence in a metric space X, converges to L ∈ X. Show, if...
Suppose (an), a sequence in a metric space X, converges to L ∈ X. Show, if σ : N → N is one-one, then the sequence (bn = aσ(n))n also converges to L.
Construct a sequence {sn} with the following property: For each rational number r ∈ [0, 1],...
Construct a sequence {sn} with the following property: For each rational number r ∈ [0, 1], {sn} has a subsequence converging to r.
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.
Give a sequence of rational numbers that converges to √5 (i.e. converges to L where L^2=5)....
Give a sequence of rational numbers that converges to √5 (i.e. converges to L where L^2=5). No proof needed.
Let {s_n} be a sequence of positive numbers. Show that the condition lim as n-> infinity...
Let {s_n} be a sequence of positive numbers. Show that the condition lim as n-> infinity of (s_n+1)/(s_n) < 1 implies s_n -> 0
Let (sn) be a sequence. Consider the set X consisting of real numbers x∈R having the...
Let (sn) be a sequence. Consider the set X consisting of real numbers x∈R having the following property: There exists N∈N s.t. for all n > N, sn< x. Prove that limsupsn= infX.
A sequence is a list of numbers that are calculated based on a certain rule. For...
A sequence is a list of numbers that are calculated based on a certain rule. For instance, the progression described by the rule An = 2 ∗ n results in the numbers: 0 2 4 6 8 10 ··· 2 ∗ n. The sum of this sequence can be calculated as Sn = 0+2+4+6+8+10+···+2 ∗ n. Write a function that takes as input the number n and calculates the sum of the sequence up to the nth term (inclusive) for...
Claim: If (sn) is any sequence of real numbers with ??+1 = ??2 + 3?? for...
Claim: If (sn) is any sequence of real numbers with ??+1 = ??2 + 3?? for all n in N, then ?? ≥ 0 for all n in N. Proof: Suppose (sn) is any sequence of real numbers with ??+1 = ??2 + 3?? for all n in N. Let P(n) be the inequality statements ?? ≥ 0. Let k be in N and suppose P(k) is true: Suppose ?? ≥ 0. Note that ??+1 = ??2 + 3?? =...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT