Divergence test

Divergence test

In this lesson, we will learn about the divergence test. The test states that if you take the limit of the general term of the series and it does not equal to 0, then the series diverge. Keep in mind that if you do take the limit and it goes to 0, that does not mean the series is convergent. It only means the test has failed, and you will have to use another method to find the convergence or divergence of the series. It is recommended to use the divergence test if u can obviously see that the limit of the general term goes to infinity. For the first few questions, we will see if the divergence test applies to the series. For the last question, we will see if the series is convergent or divergent by using the test.
Basic Concepts: Introduction to infinite series, Convergence and divergence of normal infinite series

Lessons

Note *The divergence test states the following:
If lim⁡\limn →∞\infty aann ≠\neq 0, then the series ∑an\sum a_n diverges.
  • Introduction
    Divergence Test Overview
  • 1.
    Understanding of the Divergence Test
    Does the divergence test work for the following series?
    a)
    ∑n=1∞10n \sum_{n=1}^{\infty}\frac{10}{n}

    b)
    ∑n=4∞n2+n3n3+1 \sum_{n=4}^{\infty}\frac{n^2+n^3}{n^3+1}

    c)
    ∑n=2∞n−1ln(n) \sum_{n=2}^{\infty}\frac{n-1}{ln(n)}

  • 2.
    Advanced Question Regarding to the Divergence Test
    Determine if the series ∑k=1∞k−1k3 \sum_{k=1}^{\infty}k^{-\frac{1}{k^3}} converges or diverges.
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5.
Sequence and Series
5.1
Introduction to sequences
5.2
Monotonic and bounded sequences
5.3
Introduction to infinite series
5.4
Convergence and divergence of normal infinite series
5.5
Convergence & divergence of geometric series
5.6
Convergence & divergence of telescoping series
5.7
Divergence of harmonic series
5.8
P Series
5.9
Alternating series test
5.10
Divergence test
5.11
Comparison & limit comparison test
5.12
Integral test
5.13
Ratio test
5.14
Root test
5.15
Absolute & conditional convergence
5.16
Radius and interval of convergence with power series
5.17
Functions expressed as power series
5.18
Taylor series and Maclaurin series
5.19
Approximating functions with Taylor polynomials and error bounds
Calculus 2
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