Question

For Xn given by the following, prove the convergence or divergence of the sequence (Xn) with...

For Xn given by the following, prove the convergence or divergence of the sequence (Xn) with a formal proof, clearly and neatly:

a) Xn = n2/(2n2+1)

b) Xn = (-1)n/(n+1)

c) Xn = sin(n)/(n2+1)

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Please prove the following (using epsilon/delta proofs) formally and clearly: For Xn given by the following,...
Please prove the following (using epsilon/delta proofs) formally and clearly: For Xn given by the following, prove the convergence or divergence of the sequence (Xn): a) Xn = n2/(2n2+1) b) Xn = (-1)n/(n+1) c) Xn = sin(n)/(n2+1)
1. Determine the convergence or divergence of the sequence with given ??h term (a) an=4-5/(n^2+1) (b)...
1. Determine the convergence or divergence of the sequence with given ??h term (a) an=4-5/(n^2+1) (b) an= 1/√? (c) an= (sin√?)/ √?
Determine the Convergence or Divergence of the sequence with the given n- th term. If the...
Determine the Convergence or Divergence of the sequence with the given n- th term. If the converges find the limit. a.) an= (-3/7)n+4 b.) an= nsin(1/n) c.) an= cos n?
Given that xn is a sequence of real numbers. If (xn) is a convergent sequence prove...
Given that xn is a sequence of real numbers. If (xn) is a convergent sequence prove that (xn) is bounded. That is, show that there exists C > 0 such that |xn| less than or equal to C for all n in N.
Prove the following clearly, neatly and step-by-step: Let X1=1. Define Xn+1 = sqrt(3+Xn). Show that (Xn)...
Prove the following clearly, neatly and step-by-step: Let X1=1. Define Xn+1 = sqrt(3+Xn). Show that (Xn) is convergent (by using delta/epsilon proof) and then find its limit.
If (xn) ∞ to n=1 is a convergent sequence with limn→∞ xn = 0 prove that...
If (xn) ∞ to n=1 is a convergent sequence with limn→∞ xn = 0 prove that lim n→∞ (x1 + x2 + · · · + xn)/ n = 0 .
) Let α be a fixed positive real number, α > 0. For a sequence {xn},...
) Let α be a fixed positive real number, α > 0. For a sequence {xn}, let x1 > √ α, and define x2, x3, x4, · · · by the following recurrence relation xn+1 = 1 2 xn + α xn (a) Prove that {xn} decreases monotonically (in other words, xn+1 − xn ≤ 0 for all n). (b) Prove that {xn} is bounded from below. (Hint: use proof by induction to show xn > √ α for all...
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
Use the Divergence Criterion to prove that the sequence an = (−1)n + 1 n diverges.
Use the Divergence Criterion to prove that the sequence an = (−1)n + 1 n diverges.
Use the definition of a Cauchy sequence to prove that the sequence defined by xn =...
Use the definition of a Cauchy sequence to prove that the sequence defined by xn = (3/2)^n is a Cauchy sequence in R.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT