Question

suppose that the sequence (sn) converges to s. prove that if s > 0 and sn...

suppose that the sequence (sn) converges to s. prove that if s > 0 and sn >= 0 for all n, then the sequence (sqrt(sn)) converges to sqrt(s)

Homework Answers

Answer #1

Here we have use sqrt(x) as continuous function to prove the following result.

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
suppose (Sn) converges to s and (tn) converges to t. use the definition of convergence of...
suppose (Sn) converges to s and (tn) converges to t. use the definition of convergence of sequences to prove that (sn+tn) converges to s+t.
Let (sn) ⊂ (0, +∞) be a sequence of real numbers. Prove that liminf 1/Sn =...
Let (sn) ⊂ (0, +∞) be a sequence of real numbers. Prove that liminf 1/Sn = 1 / limsup Sn
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
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.
Prove that if a sequence is a Cauchy sequence, then it converges.
Prove that if a sequence is a Cauchy sequence, then it converges.
Prove that a sequence (un such that n>=1) absolutely converges if the limit as n approaches...
Prove that a sequence (un such that n>=1) absolutely converges if the limit as n approaches infinity of n2un=L>0
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 that if a sequence converges to a limit x then very subsequence converges to x.
Prove that if a sequence converges to a limit x then very subsequence converges to x.
prove that a sequence converges if and only if all subsequences converge to the same limit
prove that a sequence converges if and only if all subsequences converge to the same limit
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