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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,
Tests for Convergence, Pt. 2
Section 11.5 – Testing for Convergence at Endpoints.
What is the sum of the following infinite series 1+x+x2+x3+…xn… where 0
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.
(a) an ordered list of objects.
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.
Math Calculus I Part VII: More tests for convergence; Power series.
Infinite Sequences and Series
INFINITE SEQUENCES AND SERIES
Math Calculus I August 9 (but first, a quick review…)
Series: Guide to Investigating Convergence. Understanding the Convergence of a Series.
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.
Section 11-1 Sequences and Series. Definitions A sequence is a set of numbers in a specific order 2, 7, 12, …
Why is it the second most important theorem in calculus?
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