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10.4 The Divergence and Integral Test Math 6B Calculus II
The Divergence Test
The Integral Test Suppose f is a continuous, positive, decreasing function on and let a k = f (k). Then the series is convergent if and only if the improper integral is convergent.
The Integral Test In other words:
p - Series Q: Does the series converge? (p is constant) A:It depends on what p is, lets look at p >1, p < 1, p = 1.
p - Series
Estimating the Sum of a Series
Furthermore, the exact value of the series is bounded as follow:
Properties of Convergent Series
Solved problems on integral test and harmonic series.
The Comparison Test Let 0 a k b k for all k.. Mika Seppälä The Comparison Test Comparison Theorem A Assume that 0 a k b k for all k. If the series converges,
Lesson 4 – P-Series General Form of P-Series is:.
Sec 11.3: THE INTEGRAL TEST AND ESTIMATES OF SUMS a continuous, positive, decreasing function on [1, inf) Convergent THEOREM: (Integral Test) Convergent.
What’s Your Guess? Chapter 9: Review of Convergent or Divergent Series.
In this section, we will define what it means for an integral to be improper and begin investigating how to determine convergence or divergence of such.
Theorems on divergent sequences. Theorem 1 If the sequence is increasing and not bounded from above then it diverges to +∞. Illustration =
Convergence or Divergence of Infinite Series
12 INFINITE SEQUENCES AND SERIES The Comparison Tests In this section, we will learn: How to find the value of a series by comparing it with a known.
Why is it the second most important theorem in calculus?
10.2 Sequences Math 6B Calculus II. Limit of Sequences from Limits of Functions.
Chapter 8-Infinite Series Calculus, 2ed, by Blank & Krantz, Copyright 2011 by John Wiley & Sons, Inc, All Rights Reserved.
8.8 Improper Integrals Math 6B Calculus II. Type 1: Infinite Integrals Definition of an Improper Integral of Type 1 provided this limit exists (as a.
Goal: Does a series converge or diverge? Lecture 24 – Divergence Test 1 Divergence Test (If a series converges, then sequence converges to 0.)
The comparison tests Theorem Suppose that and are series with positive terms, then (i) If is convergent and for all n, then is also convergent. (ii) If.
Section 9.2 – Series and Convergence. Goals of Chapter 9.
THE INTEGRAL TEST AND ESTIMATES OF SUMS
Integral Test So far, the n th term Test tells us if a series diverges and the Geometric Series Test tells us about the convergence of those series.
divergent 2.absolutely convergent 3.conditionally convergent.
Alternating Series An alternating series is a series where terms alternate in sign.
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