### Blogroll

### Archives

- August 2011 (16)
- June 2011 (5)
- May 2011 (30)
- April 2011 (4)

### Categories

Absolute Convergence Algebra Analysis Cauchy Center Compact Comparison Test Continuity Countable Cyclic Dense Differentiable Field Group Integral Domain Linear Operator Math MVT Order Principal Ideal Riemann Integrable Sequence Sequence of Functions Series Series of Functions Squeeze Theorem Topology Uncategorized Uniform Continuity Uniform Convergence

# Category Archives: Cauchy

## Rudin: Ch. 3 #8

Problem Statement: If converges and is monotonic and bounded, prove that converges. Proof: Since we are given that is bounded and monotonic we know there exists some such that . Let , then there exists some such that for every . Note that … Continue reading

## May 1999 #5

Problem Statement: Let be a real valued differentiable function on whose derivative is bounded on . Show that converges. Proof: First note that for every . Furthermore we know that is bounded so there exists a real number such that for every … Continue reading

Posted in Analysis, Cauchy, Differentiable, Math, MVT
Leave a comment

## Winter 1995

Problem Statement: Let and let for all and for every . Show that if converges then converges uniformly on . Note: This is asking us to prove the Weierstrass M-Test. Proof: Let and for every and for every . Assume that converges. … Continue reading

Posted in Analysis, Cauchy, Math, Sequence, Series of Functions, Uniform Convergence
1 Comment

## September 1999 #1

Problem Statement: Let be a sequence of non-negative real numbers. Assume there exists a real number such that converges. Show converges. Proof: Let be a sequence of non-negative real numbers. We know there exists a real number such that converges. Since the … Continue reading

Posted in Analysis, Cauchy, Comparison Test, Math, Sequence, Series
Leave a comment