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Mathematical Analysis 2 Lecture 1 - Infinite series. Series without negative terms. Convergence tests. Alternating series
1.
Mathematical Analysis 2Lecture 1 - Infinite series.
Series without negative terms. Convergence tests.
Alternating series.
Akbota Myrzakul
a.myrzakul@astanait.edu.kz
Astana IT University
2.
Lecture overview• Infinite series
• Convergence of infinite series.
• Absolutely convergent series
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Infinite series4.
Infinite series5.
Infinite series6.
Convergence of infinite seriesDefinition: E
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Convergence of infinite series8.
Convergence of infinite series9.
Convergence of a Geometric SeriesGeometric series: A series of the form
…
is called the geometric series.
Theorem
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Convergence of infinite series11.
Convergence of infinite series12.
Convergence of infinite seriesExample:
Proof:
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Convergence of infinite seriesCont…
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Convergence of infinite seriesTheorem:
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Convergence of infinite seriesExample:
Solution:
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Absolutly convergence of infinite seriesDefinition:
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Absolutely convergence of infinite seriesDetermine whether the series
converge absolutely or not ?
Solution
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Absolutly convergence of infinite seriesTheorem:
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Convergence of p-Series20.
Limit of nth Term of a Convergent Series21.
The Integral Test22.
The Integral Test23.
The Integral Test24.
Direct Comparison Test25.
Direct Comparison Test26.
Limit Comparison Test27.
Limit Comparison Test28.
Ratio Test29.
Ratio Test30.
Ratio Test31.
Root Test32.
Root Test33.
Alternating Series34.
Alternating Series35.
Absolute and Conditional Convergence36.
Absolute and Conditional Convergence37.
Guidelines for Testing a Series for Convergence orDivergence
38.
Lecture Summary• Introduction to series
• Limit of series
• Infinite series
• Convergence of infinite series.
• Absolutely convergent series