Exam Practice
Practice multiple choice questions and flashcards covering Mathematical Induction, Sequences, and Infinite Series.
Reference text: Calculus: Early Transcendentals, Stewart / SIT Lecture Notes
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Mathematical Induction
Principle of Mathematical Induction
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Definition
If P(1) is true and P(k) => P(k+1) for all k >= 1, then P(n) is true for all positive integers n.
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Sequences
Monotone Convergence Theorem
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Definition
Every bounded, monotonic sequence of real numbers is convergent.
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Series Convergence Tests
p-Series Test
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Definition
The series sum 1/n^p converges if p > 1 and diverges if p <= 1.
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Power Series
Radius of Convergence
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Definition
A non-negative number R such that the power series converges for |x - c| < R and diverges for |x - c| > R.
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