Investigate infinite sequences and test for convergence of infinite series
Sub Category
- Math
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Objectives
- Express a sequence as an order of numbers
- Express an order of numbers as a sequence
- Determine whether a sequence converges or diverges
- Prove whether a sequence is monotonic or bounded
- Find the convergence of a sequence
- Express a series in sigma notation
- Find the sum of a geometric or telescoping series
- Test for the convergence of a series using the Test for Divergence, Integral Test, Comparison/Limit Comparison Tests, Alternating Test, Root and Ratio Tests
- Estimate the Sum of a Series
- Estimate the Sum of an Alternating Series
- Find the radius of convergence and interval of convergence of a power series
- Represent a function as a Taylor Series and Maclaurin Series
- Estimate how close the function is to its Taylor series representation using the Taylor's Inequality
- Apply the Taylor polynomials
Pre Requisites
- Precalculus (algebra, trigonometry, and functions)
- Calculus 1 (limits and derivatives)
- Calculus 2 (integrals)
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